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class Constraint(enum.Enum): MEMORY = 1 TIME = 2 def __repr__(self) -> str: return self.name
def initial_divide(graph: Graph, k: int, weights: Dict[(SimpleNode, float)]) -> Tuple[(int, ...)]: random_topo_sort = random_Khan_algorithm(graph) weights = np.asarray([weights[n] for n in random_topo_sort]) cumulative_weights = np.cumsum(weights) total_weight = cumulative_weights[(- 1)] avg_weight = (total_weight / k) Vs = [] options = [math.floor(avg_weight), math.ceil(avg_weight)] acc = 0 while (len(Vs) < (k - 1)): stage_weight = options[random.randint(0, 1)] acc += stage_weight Vs.append(np.searchsorted(cumulative_weights, acc)) idxs = (([(- 1)] + Vs) + [(len(cumulative_weights) - 1)]) idxs = list(zip(map((lambda i: (i + 1)), idxs), idxs[1:])) order = [n.id for n in random_topo_sort] for (i, (start, end)) in enumerate(idxs): for n in random_topo_sort[start:(end + 1)]: n.stage_id = i return tuple(order)
def random_Khan_algorithm(graph: Graph): S = [] T = [] degs = dict() nodes = list(graph.nodes) random.shuffle(nodes) for n in nodes: if (len(n.in_edges) == 0): S.append(n) else: degs[n] = len(n.in_edges) while S: idx = random.randint(0, (len(S) - 1)) n = S[idx] del S[idx] T.append(n) for o in n.out_edges: degs[o] -= 1 if (degs[o] == 0): S.append(o) assert (len(T) == len(nodes)), 'cycle detected' return T
def simple_moves(constraint: Constraint, objective: Objective, stage_volumes: Dict[(int, float)], params_per_stage: Dict[(int, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], node_weights: Dict[(SimpleNode, float)], params_per_node: Dict[(SimpleNode, float)], L_max: float, rounds: int): connections = VerticeStageConnections(node_weights) def update_function(v: SimpleNode, dst: int): stage_volumes[v.stage_id] -= node_weights[v] stage_volumes[dst] += node_weights[v] params_per_stage[v.stage_id] -= params_per_node[v] params_per_stage[dst] += params_per_node[v] connections.move_node(v, dst) v.stage_id = dst satisfies_constraint = CONSTRAINTS[constraint] gain_function = GAINS[objective] state = PartitionState(stage_volumes, params_per_stage, node_weights, edge_weights, params_per_node, connections, L_max) k = (len(stage_volumes) - 1) nodes = list(node_weights.keys()) for _ in range(rounds): changed = False random.shuffle(nodes) for n in nodes: gain_left = (- np.inf) if ((n.stage_id > 0) and (not connections.has_in_connection(n, n.stage_id)) and satisfies_constraint(n, (n.stage_id - 1), state)): gain_left = gain_function(n, (n.stage_id - 1), state) gain_right = (- np.inf) if ((n.stage_id < k) and (not connections.has_out_connection(n, n.stage_id)) and satisfies_constraint(n, (n.stage_id + 1), state)): gain_right = gain_function(n, (n.stage_id + 1), state) moves = defaultdict(list) moves[gain_left].append((n.stage_id - 1)) moves[gain_right].append((n.stage_id + 1)) max_gain = max(moves.keys()) if (max_gain < 0): continue changed = True best_moves = moves[max_gain] dst = random.sample(best_moves, 1)[0] update_function(n, dst) if (not changed): break
def advanced_moves(constraint: Constraint, objective: Objective, stage_volumes: Dict[(int, float)], params_per_stage: Dict[(int, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], node_weights: Dict[(SimpleNode, float)], params_per_node: Dict[(SimpleNode, float)], L_max: float, rounds: int): connections = VerticeStageConnections(node_weights.keys()) def update_function(v: SimpleNode, dst: int): stage_volumes[v.stage_id] -= node_weights[v] stage_volumes[dst] += node_weights[v] params_per_stage[v.stage_id] -= params_per_node[v] params_per_stage[dst] += params_per_node[v] connections.move_node(v, dst) v.stage_id = dst satisfies_constraint = CONSTRAINTS[constraint] gain_function = GAINS[objective] state = PartitionState(stage_volumes, params_per_stage, node_weights, edge_weights, params_per_node, connections, L_max) nodes = list(node_weights.keys()) for _ in range(rounds): changed = False random.shuffle(nodes) for n in nodes: A = max((i.stage_id for i in n.in_edges), default=n.stage_id) B = min((o.stage_id for o in n.out_edges), default=n.stage_id) if (A == B): continue moves = defaultdict(list) for dst in range(A, (B + 1)): if (dst == n.stage_id): continue gain = (- np.inf) if satisfies_constraint(n, dst, state): gain = gain_function(n, dst, state) moves[gain].append(dst) max_gain = max(moves.keys()) if (max_gain < 0): continue changed = True best_moves = moves[max_gain] dst = random.sample(best_moves, 1)[0] update_function(n, dst) if (not changed): break
def global_moves(constraint: Constraint, objective: Objective, stage_volumes: Dict[(int, float)], params_per_stage: Dict[(int, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], node_weights: Dict[(SimpleNode, float)], params_per_node: Dict[(SimpleNode, float)], L_max: float, rounds: int): connections = VerticeStageConnections(node_weights.keys()) quotient_graph = QuotientGraph(node_weights.keys()) def update_function(v: SimpleNode, dst: int): stage_volumes[v.stage_id] -= node_weights[v] stage_volumes[dst] += node_weights[v] params_per_stage[v.stage_id] -= params_per_node[v] params_per_stage[dst] += params_per_node[v] connections.move_node(v, dst) quotient_graph.move_node(v, dst) satisfies_constraint = CONSTRAINTS[constraint] gain_function = GAINS[objective] state = PartitionState(stage_volumes, params_per_stage, node_weights, edge_weights, params_per_node, connections, L_max) nodes = list(node_weights.keys()) for _ in range(rounds): changed = False random.shuffle(nodes) for n in nodes: moves = defaultdict(list) for dst in stage_volumes.keys(): if (dst == n.stage_id): continue gain = (- np.inf) if (satisfies_constraint(n, dst, state) and (not quotient_graph.move_creates_cycle(n, dst))): gain = gain_function(n, dst, state) moves[gain].append(dst) max_gain = max(moves.keys()) if (max_gain < 0): continue changed = True best_moves = moves[max_gain] dst = random.sample(best_moves, 1)[0] update_function(n, dst) if (not changed): break
def Fiduccia_Mattheyses_moves(constraint: Constraint, objective: Objective, stage_volumes: Dict[(int, float)], params_per_stage: Dict[(int, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], node_weights: Dict[(SimpleNode, float)], params_per_node: Dict[(SimpleNode, float)], L_max: float, rounds: int): connections = VerticeStageConnections(node_weights.keys()) partitions = {i: set() for i in stage_volumes} for n in node_weights: partitions[n.stage_id].add(n) def update_function(v: SimpleNode, dst: int): stage_volumes[v.stage_id] -= node_weights[v] stage_volumes[dst] += node_weights[v] partitions[v.stage_id].discard(v) partitions[dst].add(v) params_per_stage[v.stage_id] -= params_per_node[v] params_per_stage[dst] += params_per_node[v] connections.move_node(v, dst) v.stage_id = dst satisfies_constraint = CONSTRAINTS[constraint] gain_function = GAINS[objective] state = PartitionState(stage_volumes, params_per_stage, node_weights, edge_weights, params_per_node, connections, L_max) if (objective is Objective.EDGE_CUT): best_objective = calculate_edge_cut(edge_weights) elif STAGE_TIME_MSE: avg_compute = (sum(stage_volumes.values()) / len(stage_volumes)) best_objective = (sum((((t - avg_compute) ** 2) for t in stage_volumes.values())) / len(stage_volumes)) else: best_objective = max(stage_volumes.values()) all_blocks = list(stage_volumes.keys()) for _ in range(rounds): active_blocks = set(all_blocks) while active_blocks: (A, B) = random.sample(all_blocks, 2) if (A > B): (A, B) = (B, A) if ((A == B) or (not ((A in active_blocks) or (B in active_blocks)))): continue active_blocks.discard(A) active_blocks.discard(B) candidate_moves = PriorityQueue() for node in partitions[A]: if all(((o.stage_id >= B) for o in node.out_edges)): candidate_moves.push_task(gain_function(node, B, state), (node, B)) for node in partitions[B]: if all(((i.stage_id <= A) for i in node.in_edges)): candidate_moves.push_task(gain_function(node, A, state), (node, A)) locked_nodes = set() moves_to_best = dict() current_objective = best_objective while (len(candidate_moves) > 0): (node, dst) = candidate_moves.pop_task() if (node in locked_nodes): continue elif (not satisfies_constraint(node, dst, state)): continue elif ((node.stage_id == A) and any(((o.stage_id < B) for o in node.out_edges))): continue elif ((node.stage_id == B) and any(((i.stage_id > A) for i in node.in_edges))): continue locked_nodes.add(node) if (objective is Objective.EDGE_CUT): current_objective -= gain_function(node, dst, state) elif STAGE_TIME_MSE: current_objective -= gain_function(node, dst, state) src = node.stage_id update_function(node, dst) if ((objective is Objective.STAGE_TIME) and (not STAGE_TIME_MSE)): current_objective = max(stage_volumes.values()) if (current_objective < best_objective): best_objective = current_objective moves_to_best.clear() active_blocks.add(A) active_blocks.add(B) else: moves_to_best[node] = src if (src == A): for i in node.in_edges: if ((i.stage_id == A) and all(((o.stage_id >= B) for o in i.out_edges))): gain = gain_function(i, B, state) candidate_moves.push_task(gain, (i, B)) else: for o in node.out_edges: if ((o.stage_id == B) and all(((i.stage_id <= A) for i in o.in_edges))): gain = gain_function(o, A, state) candidate_moves.push_task(gain, (o, A)) for (n, dst) in moves_to_best.items(): update_function(n, dst) current_objective = best_objective
class PartitionState(NamedTuple): stage_volumes: Dict[(int, float)] params_per_stage: Dict[(int, float)] node_weights: Dict[(SimpleNode, float)] edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)] params_per_node: Dict[(SimpleNode, float)] connections: VerticeStageConnections L_max: float
def calculate_edge_gain(v: SimpleNode, dst: int, state: PartitionState) -> float: edge_weights = state.edge_weights gain = 0 comm_deltas = defaultdict((lambda : 0)) connections = state.connections src = v.stage_id for u in v.in_edges: w = edge_weights[(u, v)] if (u.stage_id == src): if (not connections.has_out_connection(u, dst)): gain -= w comm_deltas[src] += w comm_deltas[dst] += w elif (u.stage_id == dst): if (connections.out_connections(u, src) == 1): gain += w comm_deltas[src] -= w comm_deltas[dst] -= w else: if (connections.out_connections(u, src) == 1): gain += w comm_deltas[u.stage_id] -= w comm_deltas[src] -= w if (not connections.has_out_connection(u, dst)): gain -= w comm_deltas[u.stage_id] += w comm_deltas[dst] += w visited = set() for o in v.out_edges: w = edge_weights[(v, o)] if (o.stage_id in visited): continue visited.add(o.stage_id) if (o.stage_id == src): gain -= w comm_deltas[src] += w comm_deltas[dst] += w elif (o.stage_id == dst): gain += w comm_deltas[src] -= w comm_deltas[dst] -= w else: comm_deltas[src] -= w comm_deltas[dst] += w return gain
def calculate_edge_cut(edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)]) -> float: edge_cut = 0 visited = set() for ((u, v), w) in edge_weights.items(): if ((u.stage_id != v.stage_id) and ((u.id, v.stage_id) not in visited)): visited.add((u.id, v.stage_id)) edge_cut += w return edge_cut
def calculate_stage_time_gain(v: SimpleNode, dst: int, state: PartitionState, use_mse=STAGE_TIME_MSE) -> float: node_weights = state.node_weights volumes = state.stage_volumes if (not use_mse): assert (not STAGE_TIME_MSE) prev_max = max(volumes[v.stage_id], volumes[dst]) new_max = max((volumes[v.stage_id] - node_weights[v]), (volumes[dst] + node_weights[v])) gain = (prev_max - new_max) else: assert STAGE_TIME_MSE avg_compute = (sum(volumes.values()) / len(volumes)) before_squared_distance = (((volumes[v.stage_id] - avg_compute) ** 2) + ((volumes[dst] - avg_compute) ** 2)) after_squared_distance = ((((volumes[v.stage_id] - node_weights[v]) - avg_compute) ** 2) + (((volumes[dst] + node_weights[v]) - avg_compute) ** 2)) gain = (before_squared_distance - after_squared_distance) return gain
def calculate_stage_times(node_weights: Dict[(SimpleNode, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], include_comm: bool=False) -> Dict[(int, float)]: stage_times = defaultdict((lambda : 0)) for (n, w) in node_weights.items(): stage_times[n.stage_id] += w if include_comm: destinations = set() for o in n.out_edges: if ((o.stage_id == n.stage_id) or (o.stage_id in destinations)): continue e = edge_weights[(n, o)] destinations.add(o.stage_id) stage_times[n.stage_id] += e stage_times[o.stage_id] += e return dict(stage_times)
def caclculate_comm_per_stage(edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)]) -> Dict[(int, float)]: comm_per_stage = defaultdict((lambda : 0)) visited = set() for ((u, v), w) in edge_weights.items(): if ((u.stage_id != v.stage_id) and ((u.id, v.stage_id) not in visited)): visited.add((u.id, v.stage_id)) comm_per_stage[u.stage_id] += w comm_per_stage[v.stage_id] += w return comm_per_stage
def calculate_params_per_node(model: Module, graph: Graph) -> Dict[(int, float)]: layers = layerDict(model, graph.depth, graph.basic_blocks) tensors = tensorDict(model) params_per_node = dict() for n in graph.nodes: if (n.scope in layers): params_per_node[n.id] = sum((t.numel() for t in layers[n.scope].parameters())) elif ((n.value_type is Parameter) and (n.scope in tensors)): params_per_node[n.id] = tensors[n.scope].numel() else: params_per_node[n.id] = 0 return params_per_node
def calculate_params_per_stage(params_per_node: Dict[(SimpleNode, float)]) -> Dict[(int, float)]: params_per_stage = defaultdict((lambda : 0)) for (n, p) in params_per_node.items(): params_per_stage[n.stage_id] += p return dict(params_per_stage)
def move_satisfies_time_constraint(v: SimpleNode, dst: int, state: PartitionState) -> bool: node_weights = state.node_weights volumes = state.stage_volumes return ((volumes[dst] + node_weights[v]) < state.L_max)
def move_satisifies_memory_constraint(v: SimpleNode, dst: int, state: PartitionState) -> bool: params_per_node = state.params_per_node params_per_stage = state.params_per_stage return ((params_per_stage[dst] + params_per_node[v]) < state.L_max)
def acyclic_partition(model: Module, graph: Graph, k: int, epsilon: float=0.1, node_weight_function: Optional[NodeWeightFunction]=None, edge_weight_function: Optional[EdgeWeightFunction]=None, constraint: Constraint=Constraint.TIME, objective: Objective=Objective.EDGE_CUT, meta_algorithm: META_ALGORITH=META_ALGORITH.SINGLE_LEVEL, maximum_constraint_value: Optional[float]=None, rounds: int=10, allocated_seconds: int=20, use_layers_graph: bool=True) -> Graph: if (node_weight_function is None): warnings.warn('using dummy weight function') node_weight_function = DefaultWeightFunction() if (edge_weight_function is None): warnings.warn('using dummy weight function') edge_weight_function = DefaultEdgeWeightFunction() if use_layers_graph: (work_graph, lookup) = graph.new_graph_without_constants() else: work_graph = graph params_per_node = calculate_params_per_node(model, work_graph) worker_args = [dict(graph=work_graph.get_copy_without_parallel_edges().state(), params_per_node=params_per_node, k=k, meta_algorithm=meta_algorithm, algorithm=alg, epsilon=epsilon, node_weight_function=node_weight_function, edge_weight_function=edge_weight_function, rounds=rounds, allocated_seconds=allocated_seconds, objective=objective, constraint=constraint, maximum_constraint_value=maximum_constraint_value) for alg in ALGORITHM] with Pool(len(worker_args)) as pool: results = pool.map(worker, worker_args) assert (len(results) == len(worker_args)) (best_solution, edge_cut, worst_case) = (None, np.inf, np.inf) for (s, e, w) in results: if is_better_solution((e, w), (edge_cut, worst_case), objective): best_solution = s edge_cut = e worst_case = w for n in work_graph.nodes: n.stage_id = best_solution[n.id] if use_layers_graph: graph.induce_layer_partition(work_graph, lookup) assert (graph.n_stages == k) return graph
def worker(kwargs) -> Tuple[(Dict[(int, int)], float, float)]: graph = Graph.from_state(kwargs.pop('graph')) kwargs['graph'] = graph meta_algorithm = kwargs.pop('meta_algorithm') algorithm = kwargs['algorithm'] allocated_seconds = kwargs.pop('allocated_seconds') objective = kwargs['objective'] (best_solution, edge_cut, worst_case) = (None, np.inf, np.inf) nwf = kwargs.pop('node_weight_function') ewf = kwargs.pop('edge_weight_function') node_weights = dict() edge_weights = dict() params_per_node = dict(kwargs['params_per_node']) for u in graph.nodes: node_weights[u] = nwf(u) params_per_node[u] = params_per_node.pop(u.id) for o in u.out_edges: edge_weights[(u, o)] = ewf(u, o) kwargs['params_per_node'] = params_per_node kwargs['node_weights'] = node_weights kwargs['edge_weights'] = edge_weights start = time.time() steps = 0 while ((time.time() - start) < allocated_seconds): seed = int.from_bytes(os.urandom(4), byteorder='little') random.seed(seed) if (meta_algorithm is META_ALGORITH.SINGLE_LEVEL): (solution, solution_edge_cut, solution_worst_case) = single_level_partitioning(**kwargs) else: (solution, solution_edge_cut, solution_worst_case) = multilevel_partitioning(**kwargs) if is_better_solution((solution_edge_cut, solution_worst_case), (edge_cut, worst_case), objective): best_solution = solution edge_cut = solution_edge_cut worst_case = solution_worst_case steps += 1 return (best_solution, edge_cut, worst_case)
def is_better_solution(solution: Tuple[(float, float)], best_solution: Tuple[(float, float)], objective: Objective) -> bool: (solution_edge_cut, solution_worst_case) = solution (best_edge_cut, best_worst_case) = best_solution better_edge_cut = (solution_edge_cut < best_edge_cut) better_worst_case = (solution_worst_case < best_worst_case) if (objective is Objective.EDGE_CUT): return (better_edge_cut or ((solution_edge_cut == best_edge_cut) and better_worst_case)) return (better_worst_case or ((solution_worst_case == best_worst_case) and better_edge_cut))
def single_level_partitioning(graph: Graph, node_weights: Dict[(SimpleNode, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], params_per_node: Dict[(SimpleNode, float)], algorithm: ALGORITHM, k: int, epsilon: float, constraint: Constraint, maximum_constraint_value: Optional[float], objective: Objective, rounds: int) -> Tuple[(Dict[(int, int)], float, float)]: if (constraint is Constraint.TIME): constraint_weights = node_weights else: constraint_weights = params_per_node initial_divide(graph, k, constraint_weights) stage_volumes = calculate_stage_times(node_weights, edge_weights, include_comm=False) params_per_stage = calculate_params_per_stage(params_per_node) if (constraint is Constraint.TIME): constraint_per_stage = stage_volumes else: constraint_per_stage = params_per_stage avg_constraint_value = (sum(constraint_per_stage.values()) / k) if (maximum_constraint_value is None): L_max = ((1 + epsilon) * math.ceil((sum(constraint_per_stage.values()) / k))) else: L_max = maximum_constraint_value msg = '\n'.join([f'-I- partitioning with {constraint.name} constraint is not possible', f' max allowed stage constraint: {L_max:.2f}', f' average constraint value: {avg_constraint_value:.2f}']) assert (avg_constraint_value < L_max), msg HEURISTICS[algorithm](constraint, objective, stage_volumes, params_per_stage, edge_weights, node_weights, params_per_node, L_max, rounds) global_moves(constraint, objective, stage_volumes, params_per_stage, edge_weights, node_weights, params_per_node, L_max, rounds=1) edge_cut = calculate_edge_cut(edge_weights) if (objective is Objective.STAGE_TIME): stage_volumes = calculate_stage_times(node_weights, edge_weights, include_comm=True) return ({n.id: n.stage_id for n in graph.nodes}, edge_cut, max(stage_volumes.values()))
def multilevel_partitioning(graph: Graph, node_weights: Dict[(SimpleNode, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], params_per_node: Dict[(SimpleNode, float)], algorithm: ALGORITHM, k: int, epsilon: float, constraint: Constraint, maximum_constraint_value: Optional[float], objective: Objective, rounds: int) -> Tuple[(Dict[(int, int)], float, float)]: single_level_partitioning(graph, params_per_node=params_per_node, node_weights=node_weights, edge_weights=edge_weights, algorithm=algorithm, k=k, epsilon=epsilon, constraint=constraint, maximum_constraint_value=maximum_constraint_value, objective=objective, rounds=rounds) stage_volumes = calculate_stage_times(node_weights, edge_weights, include_comm=False) params_per_stage = calculate_params_per_stage(params_per_node) if (constraint is Constraint.TIME): constraint_per_stage = stage_volumes else: constraint_per_stage = params_per_stage if (maximum_constraint_value is None): L_max = ((1 + epsilon) * math.ceil((sum(constraint_per_stage.values()) / k))) else: L_max = maximum_constraint_value hierarchy = coarsening(graph, node_weights, edge_weights, params_per_node) for (fine_graph, matching, coarse_graph) in reversed(hierarchy): HEURISTICS[algorithm](constraint, objective, stage_volumes, params_per_stage, coarse_graph._edge_weights, coarse_graph._node_weights, coarse_graph._params_per_node, L_max, rounds) refine(fine_graph, coarse_graph, matching) root = hierarchy[0][0] for i in range(len(graph)): graph[i].stage_id = root[i].stage_id edge_cut = calculate_edge_cut(edge_weights) if (objective is Objective.STAGE_TIME): stage_volumes = calculate_stage_times(node_weights, edge_weights, include_comm=True) return ({n.id: n.stage_id for n in graph.nodes}, edge_cut, max(stage_volumes.values()))
class DefaultWeightFunction(): def __call__(self, u: SimpleNode) -> float: return 1
class DefaultEdgeWeightFunction(): def __call__(self, u: SimpleNode, v: SimpleNode) -> float: return 1
def build_dot(node, edge_weights): '\n return a graphviz representation of the graph\n Parameters\n ----------\n ' theme = {'background_color': '#FFFFFF', 'fill_color': '#E8E8E8', 'outline_color': '#000000', 'font_color': '#000000', 'font_name': 'Times', 'font_size': '10', 'margin': '0,0', 'padding': '1.0,0.5'} from graphviz import Digraph dot = Digraph() dot.attr('graph', concentrate='true', bgcolor=theme['background_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name'], margin=theme['margin'], rankdir='TB', pad=theme['padding']) dot.attr('node', shape='box', style='filled', margin='0,0', fillcolor=theme['fill_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) dot.attr('edge', style='solid', color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) colors = {0: 'grey', 1: 'green', 2: 'red', 3: 'yellow', 4: 'orange', 5: 'brown', 6: 'purple', 7: 'pink', 8: 'cyan', 9: 'gold', 10: 'darkolivegreen', 11: 'seagreen', 12: 'thistle', 13: 'plum', 14: 'deeppink', 15: 'lightyellow', 16: 'tan'} dot.node(str(node.id), label=f'Node:{node.id}', fillcolor=colors[node.stage_id]) for i in node.in_edges: dot.node(str(i.id), label=f'Node:{i.id}', fillcolor=colors[i.stage_id]) dot.edge(str(i.id), str(node.id), label=str(edge_weights[(i, node)])) for o in node.out_edges: dot.node(str(o.id), label=f'Node:{o.id}', fillcolor=colors[o.stage_id]) dot.edge(str(node.id), str(o.id), label=str(edge_weights[(node, o)])) return dot
def show_move(node, edge_weights, file_name): dot = build_dot(node, edge_weights) dot.format = 'pdf' if os.path.exists(f'./{file_name}.pdf'): os.remove(f'./{file_name}.pdf') dot.render(file_name, directory='.', cleanup=True)
class PriorityQueue(): def __init__(self): self.heap = [] def push_task(self, gain: float, task: Any): tie_braker = random.randint(0, (2 ** 32)) priority = ((- gain), (- tie_braker)) heapq.heappush(self.heap, (priority, task)) def pop_task(self) -> Any: (priority, task) = heapq.heappop(self.heap) return task def __len__(self) -> int: return len(self.heap) def __bool__(self) -> bool: return (len(self) > 0)
class PartitionNode(): ' PartitionNode is a collection of graph nodes allocated to the same partition\n an edge exists between PartitionNodes iff they there are edges between the underlying graph nodes\n ' def __init__(self, nodes: Iterable[Node], idx: int): self.nodes: Set[Node] = set(nodes) self._out_edges = defaultdict((lambda : 0)) self._in_edges = defaultdict((lambda : 0)) self.id = idx for n in self.nodes: for i in n.in_edges: self._in_edges[i.stage_id] += 1 for o in n.out_edges: self._out_edges[o.stage_id] += 1 self._out_edges.pop(self.id, None) self._in_edges.pop(self.id, None) @property def in_edges(self) -> List[int]: return [i for (i, n) in self._in_edges.items() if (n > 0)] @property def out_edges(self) -> List[int]: return [i for (i, n) in self._out_edges.items() if (n > 0)] def __contains__(self, key) -> bool: return (key in self.nodes) def __iter__(self) -> Iterator[Node]: return iter(self.nodes) def __len__(self) -> int: return len(self.nodes) def add_in_edge(self, src: int): self._in_edges[src] += 1 def add_out_edge(self, dst: int): self._out_edges[dst] += 1 def remove_in_edge(self, src: int): self._in_edges[src] -= 1 def remove_out_edge(self, dst: int): self._out_edges[dst] -= 1 def add_node(self, node: Node): self.nodes.add(node) def remove_node(self, node: Node): self.nodes.discard(node)
class QuotientGraph(): def __init__(self, nodes: Iterable[Node]): groups = defaultdict(list) for n in nodes: groups[n.stage_id].append(n) self._nodes: Dict[(int, PartitionNode)] = {idx: PartitionNode(group, idx) for (idx, group) in groups.items()} @property def n_stages(self) -> int: return len({n.stage_id for n in self.nodes}) def __getitem__(self, idx: int) -> PartitionNode: return self._nodes[idx] def move_node(self, node: Node, dst: int): assert (node.stage_id != dst) src = node.stage_id src_part = self[src] dst_part = self[dst] src_part.remove_node(node) dst_part.add_node(node) node.stage_id = dst for i in node.in_edges: i_part = self[i.stage_id] src_part.remove_in_edge(i.stage_id) i_part.remove_out_edge(src) i_part.add_out_edge(dst) dst_part.add_in_edge(i.stage_id) for o in node.out_edges: o_part = self[o.stage_id] src_part.remove_out_edge(o.stage_id) o_part.remove_in_edge(src) o_part.add_in_edge(dst) self[dst].add_out_edge(o.stage_id) for p in self.nodes: p._in_edges.pop(p.id, None) p._out_edges.pop(p.id, None) def move_creates_cycle(self, node: Node, dest: int) -> bool: orig_part = node.stage_id self.move_node(node, dest) creates_cycle = self.has_cycles() self.move_node(node, orig_part) return creates_cycle @property def nodes(self) -> Iterable[PartitionNode]: return self._nodes.values() def has_cycles(self) -> bool: S = [] T = [] degs = dict() for n in self.nodes: assert isinstance(n, PartitionNode) if (len(n.in_edges) == 0): S.append(n.id) else: degs[n] = len(n.in_edges) while S: n = self._nodes[S.pop()] assert isinstance(n, PartitionNode) T.append(n) for o in n.out_edges: out = self._nodes[o] assert isinstance(out, PartitionNode) degs[out] -= 1 if (degs[out] == 0): S.append(o) return (len(T) < len(self.nodes)) def build_dot(self): '\n return a graphviz representation of the graph\n Parameters\n ----------\n ' theme = {'background_color': '#FFFFFF', 'fill_color': '#E8E8E8', 'outline_color': '#000000', 'font_color': '#000000', 'font_name': 'Times', 'font_size': '10', 'margin': '0,0', 'padding': '1.0,0.5'} from graphviz import Digraph dot = Digraph() dot.attr('graph', concentrate='true', bgcolor=theme['background_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name'], margin=theme['margin'], rankdir='TB', pad=theme['padding']) dot.attr('node', shape='box', style='filled', margin='0,0', fillcolor=theme['fill_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) dot.attr('edge', style='solid', color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) colors = {0: 'grey', 1: 'green', 2: 'red', 3: 'yellow', 4: 'orange', 5: 'brown', 6: 'purple', 7: 'pink', 8: 'cyan', 9: 'gold', 10: 'darkolivegreen', 11: 'seagreen', 12: 'thistle', 13: 'plum', 14: 'deeppink', 15: 'lightyellow', 16: 'tan'} for node in self.nodes: dot.node(str(node.id), label=f'partition:{node.id}', fillcolor=colors[node.id]) for i in node.in_edges: dot.edge(str(i), str(node.id)) return dot def save_as_pdf(self, file_name: str, directory: str): '\n save the rendered graph to a pdf file\n\n Parameters\n ----------\n file_name:\n the name of the saved file\n directory:\n directory to store the file in\n ' dot = self.build_dot() dot.format = 'pdf' import os if os.path.exists(f'{directory}/{file_name}.pdf'): os.remove(f'{directory}/{file_name}.pdf') dot.render(file_name, directory=directory, cleanup=True) return self def print_stats(self, node_weights: Dict[(Node, float)], edge_weights: Dict[(Tuple[(Node, Node)], float)]): volumes = defaultdict((lambda : 0)) edge_cut = 0 number_of_cutting_edges = 0 for partition in self.nodes: for n in partition: volumes[partition.id] += node_weights[n] for o in n.out_edges: if (n.stage_id != o.stage_id): if (edge_weights[(n, o)] >= 1000): print(f'{n.id}=>{o.id}') print(f'{n.stage_id}=>{o.stage_id}') print(f'{n.value_type}') print(f'''weight:{edge_weights[(n, o)]:.2f} ''') edge_cut += edge_weights[(n, o)] number_of_cutting_edges += 1 total_volume = sum(volumes.values()) avg_volume = (total_volume / len(volumes)) print(f'total number of nodes: {len(node_weights)}') print(f'total number of edges: {len(edge_weights)}') print(f'total weight: {total_volume:.2f}') print(f'avg weight: {avg_volume:.2f}') print(f'number of cutting edges: {number_of_cutting_edges}') print(f'edge cut: {edge_cut:.2f}') print('partition stats:') for i in range(len(volumes)): print(f' partition {i}') print(f' number of nodes {len(self._nodes[i])}') print(f''' partition volume: {volumes[i]:.2f} ''') def selfcheck(self): visited = set() for (idx, n) in self._nodes.items(): assert (idx == n.id) for u in n.nodes: assert (u.stage_id == idx) assert (u not in visited) visited.add(u) for (i, v) in n._in_edges.items(): assert (v >= 0), (idx, i, v) assert (idx not in n._in_edges) for i in n.in_edges: assert (idx in self._nodes[i].out_edges), (idx, i) for (o, v) in n._out_edges.items(): assert (v >= 0), (idx, o, v) assert (idx not in n._out_edges) for o in n.out_edges: assert (idx in self._nodes[o].in_edges), (idx, o) assert (not self.has_cycles())
class VerticeStageConnections(): def __init__(self, nodes): self._in_connections = dict() self._out_connections = dict() for n in nodes: self._in_connections[n] = defaultdict((lambda : 0)) self._out_connections[n] = defaultdict((lambda : 0)) for n in nodes: for u in n.in_edges: self._in_connections[n][u.stage_id] += 1 self._out_connections[u][n.stage_id] += 1 def add_in_connection(self, n, src: int): self._in_connections[n][src] += 1 def add_out_connection(self, n, dest: int): self._out_connections[n][dest] += 1 def remove_in_connection(self, n, src: int): self._in_connections[n][src] -= 1 def remove_out_connection(self, n, dest: int): self._out_connections[n][dest] -= 1 def has_in_connection(self, n, src: int) -> bool: return (self._in_connections[n][src] > 0) def has_out_connection(self, n, dest: int) -> bool: return (self._out_connections[n][dest] > 0) def in_connections(self, n, src: int) -> int: return self._in_connections[n][src] def out_connections(self, n, dst: int) -> int: return self._out_connections[n][dst] def move_node(self, n, dest: int): for u in n.in_edges: self.remove_out_connection(u, n.stage_id) self.add_out_connection(u, dest) for o in n.out_edges: self.remove_in_connection(o, n.stage_id) self.add_in_connection(o, dest)
class Path(): def __init__(self, v): self.start = self.end = v self.length = 0 self.active = True def is_cycle(self) -> bool: return ((self.start is self.end) and (self.length > 0))
class PathSet(): def __init__(self, graph_nodes: Iterable[Node]): self.paths = {v: Path(v) for v in graph_nodes} self.next: Dict[(Node, Node)] = {v: v for v in graph_nodes} self.prev: Dict[(Node, Node)] = {v: v for v in graph_nodes} self.next_edge: Dict[(Node, Optional[Tuple[(Node, Node)]])] = {v: None for v in graph_nodes} self.prev_edge: Dict[(Node, Optional[Tuple[(Node, Node)]])] = {v: None for v in graph_nodes} self.n_active_paths = len(self.paths) def is_endpoint(self, v: Node) -> bool: return ((self.next[v] is v) or (self.prev[v] is v)) def next_vertex(self, v: Node) -> Node: return self.next[v] def prev_vertex(self, v: Node) -> Node: return self.prev[v] def edge_to_next(self, v: Node) -> Optional[Tuple[(Node, Node)]]: return self.next_edge[v] def edge_to_prev(self, v: Node) -> Optional[Tuple[(Node, Node)]]: return self.prev_edge[v] def add_if_eligible(self, edge: Tuple[(Node, Node)]) -> bool: (src, dst) = edge src_path = self.paths[src] dst_path = self.paths[dst] assert (src is not dst) if (src.stage_id != dst.stage_id): return False if (not (self.is_endpoint(src) and self.is_endpoint(dst))): return False assert (src_path.active and dst_path.active) if (src_path.is_cycle() or dst_path.is_cycle()): return False if (src_path is not dst_path): self.n_active_paths -= 1 src_path.length += (dst_path.length + 1) if ((src_path.start is src) and (dst_path.start is dst)): self.paths[dst_path.end] = src_path src_path.start = dst_path.end elif ((src_path.start is src) and (dst_path.end is dst)): self.paths[dst_path.start] = src_path src_path.start = dst_path.start elif ((src_path.end is src) and (dst_path.start is dst)): self.paths[dst_path.end] = src_path src_path.end = dst_path.end elif ((src_path.end is src) and (dst_path.end is dst)): self.paths[dst_path.start] = src_path src_path.end = dst_path.start if (self.next[src] is src): assert (self.next_edge[src] is None) self.next[src] = dst self.next_edge[src] = edge else: assert (self.prev_edge[src] is None) self.prev[src] = dst self.prev_edge[src] = edge if (self.next[dst] is dst): assert (self.next_edge[dst] is None) self.next[dst] = src self.next_edge[dst] = edge else: assert (self.prev_edge[dst] is None) self.prev[dst] = src self.prev_edge[dst] = edge dst_path.active = False elif ((src_path.length % 2) == 1): src_path.length += 1 if (self.next[src_path.start] is src_path.start): self.next[src_path.start] = src_path.end self.next_edge[src_path.start] = edge else: self.prev[src_path.start] = src_path.end self.prev_edge[src_path.start] = edge if (self.next[src_path.end] is src_path.end): self.next[src_path.end] = src_path.start self.next_edge[src_path.end] = edge else: self.prev[src_path.end] = src_path.start self.prev_edge[src_path.end] = edge src_path.end = src_path.start return True return False def active_paths(self) -> Set[Path]: paths = [p for p in self.paths.values() if p.active] return set(paths)
class SimpleNode(): def __init__(self, idx, stage_id): self.id = idx self.in_edges = set() self.out_edges = set() self.stage_id = stage_id def add_in_edge(self, node): self.in_edges.add(node) def add_out_edge(self, node): self.out_edges.add(node)
class ContractedGraph(): def __init__(self, in_edges, partition, node_weights, edge_weights, params_per_node, matching): self._nodes: Dict[(int, SimpleNode)] = dict() for n in set(matching.values()): self._nodes[n] = SimpleNode(n, partition[n]) self._node_weights = defaultdict((lambda : 0)) self._edge_weights = defaultdict((lambda : 0)) self._params_per_node = defaultdict((lambda : 0)) for n in node_weights.keys(): matched = matching[n] self._node_weights[self._nodes[matched]] += node_weights[n] self._params_per_node[self._nodes[matched]] += params_per_node[n] for i in in_edges[n]: matched_i = matching[i] if (matched_i == matched): continue self._nodes[matched].add_in_edge(self._nodes[matched_i]) self._nodes[matched_i].add_out_edge(self._nodes[matched]) self._edge_weights[(self._nodes[matched_i], self._nodes[matched])] += edge_weights[(i, n)] @property def n_stages(self) -> int: return len({n.stage_id for n in self.nodes}) def __len__(self) -> int: return len(self._nodes) def __getitem__(self, idx) -> SimpleNode: return self._nodes[idx] def node_weight(self, n) -> float: return self._node_weights[n] def edge_weight(self, u, v) -> float: return self._edge_weights[(u, v)] def params_per_node(self, n) -> float: return self._params_per_node[n] @property def nodes(self) -> Iterable[SimpleNode]: return self._nodes.values() def selfcheck(self) -> 'ContractedGraph': try: for (idx, n) in self._nodes.items(): assert (n.id == idx) assert (n in self._node_weights) for u in n.in_edges: assert (n.stage_id >= u.stage_id) assert (n in u.out_edges) assert ((u, n) in self._edge_weights) assert (u in self._node_weights) assert (u.id in self._nodes) for o in n.out_edges: assert (o.stage_id >= n.stage_id) assert (n in o.in_edges) assert ((n, o) in self._edge_weights) assert (o in self._node_weights) assert (o.id in self._nodes) return self except AssertionError as e: self.save_as_pdf('selfcheck_error', '.') raise e @classmethod def contract(cls, contracted_graph, matching) -> 'ContractedGraph': in_edges = dict() partition = dict() node_weights = dict() edge_weights = dict() params_per_node = dict() for n in contracted_graph.nodes: node_weights[n.id] = contracted_graph.node_weight(n) params_per_node[n.id] = contracted_graph.params_per_node(n) partition[n.id] = n.stage_id us = set() for u in n.in_edges: us.add(u.id) edge_weights[(u.id, n.id)] = contracted_graph.edge_weight(u, n) in_edges[n.id] = us return cls(in_edges, partition, node_weights, edge_weights, params_per_node, matching) @classmethod def from_Graph(cls, graph: Graph, node_weights, edge_weights, params_per_node) -> 'ContractedGraph': node_weights = {n.id: w for (n, w) in node_weights.items()} edge_weights = {(u.id, v.id): w for ((u, v), w) in edge_weights.items()} params_per_node = {n.id: p for (n, p) in params_per_node.items()} in_edges = dict() partition = dict() for n in graph.nodes: in_edges[n.id] = {u.id for u in n.in_edges} partition[n.id] = n.stage_id initial_matching = {n: n for n in node_weights} return cls(in_edges, partition, node_weights, edge_weights, params_per_node, initial_matching) def build_dot(self): '\n return a graphviz representation of the graph\n Parameters\n ----------\n ' theme = {'background_color': '#FFFFFF', 'fill_color': '#E8E8E8', 'outline_color': '#000000', 'font_color': '#000000', 'font_name': 'Times', 'font_size': '10', 'margin': '0,0', 'padding': '1.0,0.5'} from graphviz import Digraph dot = Digraph() dot.attr('graph', concentrate='true', bgcolor=theme['background_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name'], margin=theme['margin'], rankdir='TB', pad=theme['padding']) dot.attr('node', shape='box', style='filled', margin='0,0', fillcolor=theme['fill_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) dot.attr('edge', style='solid', color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) colors = {0: 'grey', 1: 'green', 2: 'red', 3: 'yellow', 4: 'orange', 5: 'brown', 6: 'purple', 7: 'pink', 8: 'cyan', 9: 'gold', 10: 'darkolivegreen', 11: 'seagreen', 12: 'thistle', 13: 'plum', 14: 'deeppink', 15: 'lightyellow', 16: 'tan'} for node in self._nodes.values(): dot.node(str(node.id), label=f'''Node:{node.id} weight:{self.node_weight(node)}''', fillcolor=colors[node.stage_id]) for i in node.in_edges: dot.edge(str(i.id), str(node.id), label=f'weight:{self.edge_weight(i, node)}') return dot def save_as_pdf(self, file_name: str, directory: str): '\n save the rendered graph to a pdf file\n\n Parameters\n ----------\n file_name:\n the name of the saved file\n directory:\n directory to store the file in\n ' dot = self.build_dot() dot.format = 'pdf' import os if os.path.exists(f'{directory}/{file_name}.pdf'): os.remove(f'{directory}/{file_name}.pdf') dot.render(file_name, directory=directory, cleanup=True) return self
def coarsening(graph: Graph, node_weights: Dict[(SimpleNode, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)], params_per_node: Dict[(SimpleNode, float)]) -> List[Tuple[(ContractedGraph, Dict[(int, int)], ContractedGraph)]]: g = ContractedGraph.from_Graph(graph, node_weights, edge_weights, params_per_node) n = len(g) hierarchy = [] p = g while True: (matching, _) = find_max_matching(g._node_weights, g._edge_weights) g = g.contract(g, matching) if (len(g) == n): break hierarchy.append((p, matching, g)) n = len(g) p = g return hierarchy
def refine(fine_graph: ContractedGraph, coarse_graph: ContractedGraph, matching: Dict[(int, int)]): for n in fine_graph.nodes: n.stage_id = coarse_graph[matching[n.id]].stage_id
def find_max_matching(node_weights: Dict[(SimpleNode, float)], edge_weights: Dict[(Tuple[(SimpleNode, SimpleNode)], float)]) -> Tuple[(Dict[(int, int)], float)]: edges = list(edge_weights.keys()) edge_ratings = {e: edge_rating(e[0], e[1], edge_weights, node_weights) for e in edges} random.shuffle(edges) edges = sorted(edges, key=(lambda e: edge_ratings[e]), reverse=True) pathset = PathSet(node_weights.keys()) for edge in edges: pathset.add_if_eligible(edge) max_match = [] max_match_weight = 0 for node in node_weights.keys(): path = pathset.paths[node] if (not path.active): continue if (path.end is not node): continue if (path.length == 0): continue if path.is_cycle(): unpacked_cycle = unpack_path(pathset, path) first_edge = unpacked_cycle.pop(0) (match_a, match_a_weight) = max_path_matching(unpacked_cycle, edge_ratings) unpacked_cycle.insert(0, first_edge) last_edge = unpacked_cycle.pop() (match_b, match_b_weight) = max_path_matching(unpacked_cycle, edge_ratings) unpacked_cycle.append(last_edge) if (match_a_weight > match_b_weight): match = match_a match_weight = match_a_weight else: match = match_b match_weight = match_b_weight elif (path.length == 1): if (pathset.next_vertex(path.end) is path.start): edge = pathset.edge_to_next(path.end) else: edge = pathset.edge_to_prev(path.end) assert (pathset.next_vertex(path.end) is path.start) (match, match_weight) = ([edge], edge_ratings[edge]) else: unpacked_path = unpack_path(pathset, path) (match, match_weight) = max_path_matching(unpacked_path, edge_ratings) max_match.extend(match) max_match_weight += match_weight matching = {u.id: v.id for (u, v) in max_match} for n in node_weights.keys(): if (n.id not in matching): matching[n.id] = n.id return (matching, max_match_weight)
def max_path_matching(unpacked_path: List[Tuple[(Node, Node)]], edge_ratings: Dict[(Tuple[(Node, Node)], float)]) -> Tuple[(List[Tuple[(Node, Node)]], float)]: k = len(unpacked_path) if (k == 1): return (list(unpacked_path), edge_ratings[unpacked_path[0]]) ratings = ([0] * k) decision = ([False] * k) ratings[0] = edge_ratings[unpacked_path[0]] ratings[1] = edge_ratings[unpacked_path[1]] decision[0] = True if (ratings[0] < ratings[1]): decision[1] = True for i in range(2, k): cur_w = edge_ratings[unpacked_path[i]] if ((cur_w + ratings[(i - 2)]) > ratings[(i - 1)]): decision[i] = True ratings[i] = (cur_w + ratings[(i - 2)]) else: decision[i] = False ratings[i] = ratings[(i - 1)] if decision[(- 1)]: match_weight = ratings[(- 1)] else: match_weight = ratings[(- 2)] match = [] i = (k - 1) while (i >= 0): if decision[i]: match.append(unpacked_path[i]) i -= 2 else: i -= 1 return (match, match_weight)
def unpack_path(pathset: PathSet, path: Path) -> List[Tuple[(Node, Node)]]: assert path.active head = path.start prev = path.end next_v = None current = prev unpacked_path = [] if (prev is head): current = pathset.next_vertex(prev) unpacked_path.append(pathset.edge_to_next(prev)) while (current is not head): if (pathset.next_vertex(current) is prev): next_v = pathset.prev_vertex(current) unpacked_path.append(pathset.edge_to_prev(current)) else: next_v = pathset.next_vertex(current) unpacked_path.append(pathset.edge_to_next(current)) (prev, current) = (current, next_v) return unpacked_path
def edge_rating(u: Node, v: Node, edge_weights: Dict[(Tuple[(Node, Node)], float)], node_weights: Dict[(Node, float)]) -> float: return ((edge_weights[(u, v)] ** 2) / (1 + (node_weights[u] * node_weights[v])))
def visualize_matching(nodes, matching, file_name: str, directory: str): '\n return a graphviz representation of the graph\n Parameters\n ----------\n ' theme = {'background_color': '#FFFFFF', 'fill_color': '#E8E8E8', 'outline_color': '#000000', 'font_color': '#000000', 'font_name': 'Times', 'font_size': '10', 'margin': '0,0', 'padding': '1.0,0.5'} from graphviz import Digraph dot = Digraph() dot.attr('graph', concentrate='true', bgcolor=theme['background_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name'], margin=theme['margin'], rankdir='TB', pad=theme['padding']) dot.attr('node', shape='box', style='filled', margin='0,0', fillcolor=theme['fill_color'], color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) dot.attr('edge', style='solid', color=theme['outline_color'], fontsize=theme['font_size'], fontcolor=theme['font_color'], fontname=theme['font_name']) partition_color = {0: 'grey', 1: 'green', 2: 'red', 3: 'yellow', 4: 'orange', 5: 'brown', 6: 'purple', 7: 'pink', 8: 'cyan', 9: 'gold', 10: 'darkolivegreen', 11: 'seagreen', 12: 'thistle', 13: 'plum', 14: 'deeppink', 15: 'lightyellow', 16: 'tan'} def random_color(): return ('#' + ''.join([random.choice('0123456789ABCDEF') for j in range(6)])) matching_colors = set() while (len(matching_colors) < len(matching)): c = random_color() if (c not in partition_color): matching_colors.add(c) edge_colors = {(u, v): c for ((u, v), c) in zip(matching.items(), matching_colors)} for node in nodes: dot.node(str(node.id), label=node.scope, fillcolor=partition_color[node.stage_id]) for i in node.in_edges: dot.edge(str(i.id), str(node.id), color=edge_colors.get((i.id, node.id), '#000000')) dot.format = 'pdf' import os if os.path.exists(f'{directory}/{file_name}.pdf'): os.remove(f'{directory}/{file_name}.pdf') dot.render(file_name, directory=directory, cleanup=True)
def partition_and_match_weights_until_last_partition_is_with_no_recomputation(graph: Graph, weights: Dict[(Node, FullExecTimes)], partitioning_method, partition_profiled_graph_fn, n_runs_limit=10, do_exhustive_search_for_last_partition=True, max_memory_usage_r=None, max_memory_usage_nr=None): print('-I- partition_and_match_weights_until_last_partition_is_with_no_recomputation') warnings.warn('need to set max memory usage: currently doing this only for recomputation.') if max_memory_usage_r: for node in graph.nodes: if (node.scope in max_memory_usage_r): node.max_memory_bytes = max_memory_usage_r[node.scope] saved_state = graph.state() allowed_mistakes = 0 if (partitioning_method == 'ACYCLIC'): allowed_mistakes += 2 last_partition_scopes = set() current_mistakes = (allowed_mistakes + 1) n_runs = 0 history = dict() while ((current_mistakes > allowed_mistakes) and ((n_runs_limit < 0) or (n_runs < n_runs_limit))): n_runs += 1 (current_mistakes, d, generated_last_stage_scopes, graph) = partition_and_check(Graph.from_state(saved_state), last_partition_scopes, partition_profiled_graph_fn, weights) history[n_runs] = dict(last_partition_scopes=last_partition_scopes, generated_last_stage_scopes=generated_last_stage_scopes, d=d, graph_state=graph.state()) last_partition_scopes = generated_last_stage_scopes print(f'run:{n_runs}', d) if (not (current_mistakes > allowed_mistakes)): print(f'Success! got {current_mistakes} mistakes after {n_runs} runs') elif (not ((n_runs_limit < 0) or (n_runs < n_runs_limit))): print(f'Breaking after reaching run limit of {n_runs_limit}!') (current_mistakes, graph, mistakes_min) = restore_best_from_history(saved_state, history, partition_profiled_graph_fn, weights) if (current_mistakes != mistakes_min): warnings.warn(f'current_mistakes != mistakes_min, {current_mistakes} != {mistakes_min}') if ((current_mistakes > 2) and do_exhustive_search_for_last_partition): graph = exhustive_search_for_last_partition(saved_state, graph, history, n_runs, partition_profiled_graph_fn, weights, smallest_fp_with_zero_fp=True) return graph
def exhustive_search_for_last_partition(saved_state, graph, history, n_runs, partition_profiled_graph_fn, weights, smallest_fp_with_zero_fp=False): if smallest_fp_with_zero_fp: cands = [] for (i, v) in history.items(): d = v['d'] if (d['fp'] > 0): continue cands.append((i, (d['fn'], (- d['correct'])))) best = cands[0] for c in cands[1:]: if (c[1] < best): best = c possible_scopes = set(history[best[0]]['generated_last_stage_scopes']) else: possible_scopes = set(history[1]['generated_last_stage_scopes']) scope_to_id = {} for n in graph.nodes: if (n.scope in possible_scopes): scope_to_id[n.scope] = n.id topo_sorted_scopes = sorted(possible_scopes, key=(lambda x: scope_to_id[x])) print("Guessing prev-option didn't converge,") print('Doing exhaustive search over last stage IDs and taking best fit') exhaustive_search_history = dict() for i in range(len(topo_sorted_scopes)): last_partition_scopes = topo_sorted_scopes[i:] (current_mistakes, d, generated_last_stage_scopes, graph) = partition_and_check(Graph.from_state(saved_state), last_partition_scopes, partition_profiled_graph_fn, weights) exhaustive_search_history[i] = dict(last_partition_scopes=last_partition_scopes, generated_last_stage_scopes=generated_last_stage_scopes, d=d, graph_state=graph.state()) print(f'final_countdown_iteration:{i}/{len(topo_sorted_scopes)}', d) (current_mistakes, graph, mistakes_min) = restore_best_from_history(saved_state, exhaustive_search_history, partition_profiled_graph_fn, weights) return graph
def restore_best_from_history(saved_state, history, partition_profiled_graph_fn, weights): i_min = list(history.keys())[int(np.argmin([v['d']['mistakes'] for v in history.values()]))] mistakes_min = history[i_min]['d']['mistakes'] print([history[i]['d']['mistakes'] for i in history]) print(f'Restoring best point in history') print(f'Taking best seen: {mistakes_min} mistakes after {i_min} runs') min_hist = history[i_min] if ('graph_state' in min_hist): graph_state = min_hist['graph_state'] current_mistakes = mistakes_min graph = Graph.from_state(graph_state) else: print('Partitioning again to restore history') warnings.warn('must start from clear state!') last_partition_scopes = history[i_min]['last_partition_scopes'] (current_mistakes, d, generated_last_stage_scopes, graph) = partition_and_check(Graph.from_state(saved_state), last_partition_scopes, partition_profiled_graph_fn, weights) return (current_mistakes, graph, mistakes_min)
def partition_and_check(graph, last_partition_scopes, partition_profiled_graph_fn, weights): for n in graph.nodes: if (n.scope in last_partition_scopes): n.weight = weights[n.id].no_recomputation else: n.weight = weights[n.id].recomputation graph = partition_profiled_graph_fn(graph) last_p = max((n.stage_id for n in graph.nodes)) generated_last_stage_scopes = [n.scope for n in graph.nodes if (n.stage_id == last_p)] A = set(last_partition_scopes) B = set(generated_last_stage_scopes) intersection = (A & B) correct = len(intersection) fp = (len(A) - correct) fn = (len(B) - correct) current_mistakes = (fp + fn) d = dict(correct=correct, fp=fp, fn=fn, mistakes=current_mistakes) return (current_mistakes, d, generated_last_stage_scopes, graph)
def get_weight_functions(args, verbose=True): MULT_FACTOR = args.weight_mult_factor if args.auto_infer_node_bwd_to_fwd_ratio: node = NodeWeightFunctionWithRatioAutoInfer(MULT_FACTOR=MULT_FACTOR) else: node = NodeWeightFunction(bwd_to_fwd_ratio=args.bwd_to_fwd_ratio, MULT_FACTOR=MULT_FACTOR) warnings.warn('Modeling Communications of activations only. Problematic for some algorithms') edge = EdgeWeightFunction(args.bw, bwd_to_fwd_ratio=0, penalize_non_tensors=args.penalize_non_tensors, penalty=args.edge_penalty, MULT_FACTOR=MULT_FACTOR) if verbose: print(f'-I- using heuristics {type(node).__name__} , {type(edge).__name__}') return (node, edge)
class NodeWeightFunction(): def __init__(self, bwd_to_fwd_ratio=(- 1), MULT_FACTOR=10000.0): self.ratio = bwd_to_fwd_ratio self.MULT_FACTOR = MULT_FACTOR def __call__(self, node: Node): assert isinstance(node.weight, ExecTimes) if (self.ratio < 0): return (self.MULT_FACTOR * node.weight.backward_time) elif (self.ratio == 0): return (self.MULT_FACTOR * node.weight.forward_time) else: return (self.MULT_FACTOR * ((self.ratio * node.weight.backward_time) + node.weight.forward_time))
class EdgeWeightFunction(): GPU_MEMORY_BW = 550 NON_CONTIGIOUS_PENATLY = True def __init__(self, bw_GBps, bwd_to_fwd_ratio=(- 1), MULT_FACTOR=10000.0, penalty=10000000.0, penalize_non_tensors=False, ensure_positive=True): self.bw = bw_GBps self.ratio = bwd_to_fwd_ratio self.MULT_FACTOR = MULT_FACTOR self.penalty = penalty self.penalize_non_tensors = penalize_non_tensors self.ensure_positive = ensure_positive def __call__(self, u: Node, v: Node, non_contig_penalty=False): if u.compound_edge_weights: if (self.ratio == 0): if ((u.gpu_id != v.gpu_id) or ((u.gpu_id is None) and (v.gpu_id is None))): return u.compound_edge_weights[v.id] elif (u.gpu_id == v.gpu_id): warnings.warn('experimental - compound weight but on same GPU - should it happen? check it is not an output node.') return (u.compound_edge_weights[v.id] / (self.GPU_MEMORY_BW / self.bw)) else: raise NotImplementedError('not supported yet') elif (self.ratio < 0): warnings.warn('using forward activations as backward comm for merged node, ignoring req_grad=False edges') if ((u.gpu_id != v.gpu_id) or ((u.gpu_id is None) and (v.gpu_id is None))): return u.compound_edge_weights[v.id] elif (u.gpu_id == v.gpu_id): return (u.compound_edge_weights[v.id] / (self.GPU_MEMORY_BW / self.bw)) else: raise NotImplementedError('not supported yet') MB = 1000000.0 if (u.value_type in [torch.device, torch.dtype, str, slice]): w = self.penalty elif (self.penalize_non_tensors and ((u.type is NodeTypes.CONSTANT) or (u.value_type in [int, bool, float]))): w = self.penalty else: bwd_volume = 0 if ((u.type is NodeTypes.CONSTANT) or (u.value_type in [int, bool, float, torch.Size, type(None)])): volume = 4 else: volume = 0 for (shape, dtype) in zip(flatten(u.tensor_shape), flatten(u.tensor_dtype)): if isinstance(shape, torch.Size): tmp = reduce(operator.mul, shape, 1) tmp *= torch.empty(1, dtype=dtype).element_size() if (u.req_grad and v.req_grad): bwd_volume += tmp elif ((dtype is type(None)) and (not self.penalize_non_tensors)): warnings.warn('experimentally allowing None inside a tuple.') tmp = 4 else: warnings.warn(f'Unknown dtype={dtype}, type(dtype)={type(dtype)}, node:{u}. valtype:{u.value_type} PENALIZING!') return self.penalty volume += tmp if ((u.gpu_id is not None) and (v.gpu_id is not None) and (u.gpu_id == v.gpu_id)): bw = self.GPU_MEMORY_BW else: bw = self.bw volume /= (MB * bw) bwd_volume /= (MB * bw) if (self.ratio < 0): w = (self.MULT_FACTOR * bwd_volume) elif (self.ratio == 0): if ((not u.is_contiguous) and non_contig_penalty): volume += ((volume * bw) / self.GPU_MEMORY_BW) w = (self.MULT_FACTOR * volume) else: w = (self.MULT_FACTOR * (bwd_volume + volume)) return (max(0.001, w) if self.ensure_positive else w)
class NodeWeightFunctionWithRatioAutoInfer(): def __init__(self, MULT_FACTOR=10000.0): self.MULT_FACTOR = MULT_FACTOR def __call__(self, node: Node): assert isinstance(node.weight, ExecTimes) bwd = node.weight.backward_time fwd = node.weight.forward_time bwd_plus_fwd = (bwd + fwd) if (bwd_plus_fwd == 0): return 0 return ((self.MULT_FACTOR * ((bwd * bwd) + (fwd * fwd))) / bwd_plus_fwd)
class CoarsenedWeightFunction(): def __init__(self, edge_weight_function: EdgeWeightFunction, node_weight_function: NodeWeightFunction, do_critical_path=False): self.mode = 'ratio' self.do_critical_path = do_critical_path self.ewf = edge_weight_function self.nwf = node_weight_function assert (self.nwf.MULT_FACTOR == self.ewf.MULT_FACTOR) if (self.nwf.ratio != 1): raise NotImplementedError() def __call__(self, nodes: Iterable[Node], boarders: Optional[Tuple[(Set[Tuple[(Node, Node)]], Set[Node], Set[Tuple[(Node, Node)]], Set[Node])]]=None, total_gpu_comp_cost: Optional[float]=None, total_stage_comp_cost_fwd: Optional[float]=None, total_stage_comp_cost_bwd: Optional[float]=None): if boarders: (outgoing_edges, _, incomming_edges, _) = boarders else: (outgoing_edges, _, incomming_edges, _) = self.calculate_borders(nodes) if (total_gpu_comp_cost is None): (comp_bwd, comp_fwd) = self.calculate_comp(nodes) combined_comp_cost = (comp_bwd + comp_fwd) overlaped_comp_fwd = combined_comp_cost overlaped_comp_bwd = combined_comp_cost else: combined_comp_cost = total_gpu_comp_cost overlaped_comp_fwd = combined_comp_cost overlaped_comp_bwd = combined_comp_cost (comm_bwd, comm_fwd) = self.calculate_comm_forward_and_backward(incomming_edges, outgoing_edges) cost = ((combined_comp_cost + max(0, (comm_fwd - overlaped_comp_fwd))) + max(0, (comm_bwd - overlaped_comp_bwd))) return cost def is_comm_bounded_forward(self, node: Node): outgoing = [(node, nn) for nn in node.out_edges] comm = self.calculate_comm_forward(outgoing) return (self.nwf(node) <= comm) def is_comm_bounded_backward(self, node: Node): incomming = [(nn, node) for nn in node.in_edges] comm = self.calculate_comm_backward(incomming) return (self.nwf(node) <= comm) def calculate_comp(self, nodes: Iterable[Node]): if (not self.do_critical_path): comp_fwd = sum((node.weight.forward_time for node in nodes)) comp_bwd = sum((node.weight.backward_time for node in nodes)) else: raise NotImplementedError() comp_fwd *= self.nwf.MULT_FACTOR comp_bwd *= self.nwf.MULT_FACTOR return (comp_bwd, comp_fwd) @staticmethod def calculate_borders(nodes: Iterable[Node]) -> Tuple[(Set[Tuple[(Node, Node)]], Set[Node], Set[Tuple[(Node, Node)]], Set[Node])]: set_nodes = set(nodes) outgoing_edges = set() incoming_edges = set() outgoing_nodes = set() incoming_nodes = set() for node in nodes: for out in node.out_edges: if (out not in set_nodes): outgoing_edges.add((node, out)) outgoing_nodes.add(node) for inode in node.in_edges: if (inode not in set_nodes): incoming_edges.add((inode, node)) incoming_nodes.add(node) return (outgoing_edges, outgoing_nodes, incoming_edges, incoming_nodes) def is_comm_bounded(self, nodes: Set[Node], boarders: Optional[Tuple[(Set[Tuple[(Node, Node)]], Set[Node], Set[Tuple[(Node, Node)]], Set[Node])]]=None): (comp_bwd, comp_fwd) = self.calculate_comp(nodes) combined_comp_cost = (comp_bwd + comp_fwd) overlaped_comp_fwd = overlaped_comp_bwd = combined_comp_cost if boarders: (outgoing_edges, _, incomming_edges, _) = boarders else: (outgoing_edges, _, incomming_edges, _) = self.calculate_borders(nodes) (comm_bwd, comm_fwd) = self.calculate_comm_forward_and_backward(incomming_edges, outgoing_edges) is_comm_fwd = (overlaped_comp_fwd < comm_fwd) is_comm_bwd = (overlaped_comp_bwd < comm_bwd) return (is_comm_fwd, is_comm_bwd) def calculate_comm_forward_and_backward(self, incomming_edges, outgoing_edges): comm_bwd = self.calculate_comm_backward(incomming_edges) comm_fwd = self.calculate_comm_forward(outgoing_edges) return (comm_bwd, comm_fwd) def calculate_comm_forward(self, outgoing_edges): tmp = self.ewf.ratio assert (tmp == 0) comm_fwd = sum((self.ewf(*e) for e in outgoing_edges)) return comm_fwd def calculate_comm_backward(self, incomming_edges): tmp = self.ewf.ratio self.ewf.ratio = (- 1) comm_bwd = sum((self.ewf(*e) for e in incomming_edges)) self.ewf.ratio = tmp return comm_bwd
class NodeMemoryEstimator(): THRESHOLD = (11 * 1000000000.0) def __init__(self, optimizer_multiply=1): self.optimizer_multiply = optimizer_multiply @staticmethod def cuda_activations_and_grads_mem(u: Node): if ((u.type is NodeTypes.LAYER) or (u.type is NodeTypes.BUFF_PARAM)): if (u.value_type in [int, bool, float, torch.Size, type(None)]): return 0 if ((u.type is NodeTypes.CONSTANT) or (u.value_type in [torch.device, torch.dtype, str, slice])): return 0 bwd_volume = 0 volume = 0 for (shape, dtype) in zip(flatten(u.tensor_shape), flatten(u.tensor_dtype)): if isinstance(shape, torch.Size): tmp = reduce(operator.mul, shape, 1) tmp *= torch.empty(1, dtype=dtype).element_size() if u.req_grad: bwd_volume += tmp volume += tmp else: warnings.warn(f'Unknown dtype={dtype}, type(dtype)={type(dtype)}, node:{u}. ignoring volume!') return (volume + bwd_volume) else: return 0 def __call__(self, node: Node): byte_per_parameter = 4 parameter_size = ((node.num_parameters * byte_per_parameter) * self.optimizer_multiply) activations_size = node.max_memory_bytes return (activations_size + parameter_size)
def metis_partition(graph: Graph, num_partitions: int, node_weight_function: Optional[NodeWeightFunction]=None, edge_weight_function: Optional[EdgeWeightFunction]=None, use_layers_only_graph: bool=True, use_virtual_stages: bool=True, **METIS_opts: Dict) -> Graph: '\n performs METIS Kway partitioning on the given graph\n\n Parameters:\n graph:\n the Graph to partition\n num_partitions:\n the number of partitions\n node_weight_function:\n an optional weight function for the nodes should be a function from Node to int\n if not given a default weight of 1 will be given to all nodes\n edge_weight_function:\n an optional weight function for the edges should be a function (Node,Node) to int\n if not given a default value of 1 will be given to all edges\n use_layers_only_graph:\n whether to partition a smaller version of the graph containing only the layers\n (usefull fo big models with lots of unprofiled ops)\n METIS_opts:\n additional kwargs to pass to the METIS partitioning algorithm\n ' import nxmetis if use_virtual_stages: graph.topo_sort() if use_layers_only_graph: (layers_graph, layers_to_original) = graph.new_graph_without_constants() G = layers_graph else: G = graph work_graph = G G = G.asNetworkx(directed=False, node_weight_function=node_weight_function, edge_weight_function=edge_weight_function) attempts = METIS_opts.pop('attempts', 1) verbose_on_error = METIS_opts.pop('verbose_on_error', False) options = nxmetis.MetisOptions(**METIS_opts) fail = True last_exception = None for _ in range(attempts): (objval, parts) = nxmetis.partition(G, num_partitions, options=options, node_weight='weight', node_size='size', edge_weight='weight', recursive=False) parts = sorted(((idx, n) for (n, p) in enumerate(parts) for idx in p)) parts = [n for (_, n) in parts] if (not use_virtual_stages): for (node, stage_id) in zip(work_graph.nodes, parts): node.stage_id = stage_id else: unique_gpu_ids = set() bins = defaultdict(list) for (node, gpu_id) in zip(work_graph.nodes, parts): if (node in work_graph.inputs): continue node.gpu_id = gpu_id unique_gpu_ids.add(gpu_id) bins[gpu_id].append(node) nodes = [n for n in work_graph.nodes if (n not in work_graph.inputs)] graph.topo_sort(change_graph=False) id_to_node = {node.topo_sort_id: node for node in nodes} stages_from_bins(graph=work_graph, bins=bins, id_to_node_worked_on=id_to_node) try: post_process_partition(work_graph, edge_weight_function, assert_output_types=False, verbose_on_error=verbose_on_error) fail = False break except (Exception, RuntimeError, AssertionError) as e: last_exception = e if fail: print(f'-I- METIS could not find a valid partitioning') raise last_exception n_parts = set(parts) actual_nparts = len({n.stage_id for n in work_graph.nodes}) if (actual_nparts < num_partitions): print('This is deprecated....') print(f'-I- expected {num_partitions} partitions but only {actual_nparts} found implicating that the model to partition is too small') print('consider increasing the depth of graph or disabling the basic blocks option') print(f'before post processing there were {n_parts} partitions') if use_layers_only_graph: graph.induce_layer_partition(work_graph, layers_to_original) if use_virtual_stages: stage_to_gpu_map = convert_handle_missing_print(bins=bins, graph=graph, verbose=False) return graph
def post_process_partition(graph: Graph, edge_weight_function, verbose_on_error=True, assert_output_types=False) -> Graph: "\n process the partition and optimize it\n called as part of partition_graph method\n\n Parameters:\n ----------\n graph:\n the Graph object that was partitioned\n verbose_on_error:\n print extra info when cycle can't be solved\n " re_assign_partition_indices(graph) if has_stage_cycles(graph): if os.environ.get('DEBUG', False): graph.save_as_pdf(f'{graph.model_name}_before_fix', '.') if verbose_on_error: (problems, info) = get_problematic_partitions(graph) print('-V- printing problematic partitions') for (p, i) in zip(problems, info): print(p) print(i) n_partitions = len(set((u.stage_id for u in graph.nodes))) print('n_partitions:', n_partitions) error = 'error cycle detected mutual dependency between partitions' raise AssertionError(error) (is_valid, error) = is_valid_partitioning(graph, edge_weight_function) if assert_output_types: assert is_valid, error elif (not is_valid): print('Output between partitions is tricky, but allowing this') print_all_problematic_outputs_between_partitions(graph, edge_weight_function) return graph
def get_problematic_partitions(graph): ' For debug when cycle are detected ' problems = [] info = [] for u in graph.nodes: for v in u.out_edges: if (v.stage_id < u.stage_id): problems.append([v.stage_id, u.stage_id]) info.append([v.scope, u.scope]) return (problems, info)
def break_partition_cycles(graph: Graph): parts = set() roots = defaultdict(set) for u in graph.nodes: parts.add(u.stage_id) for v in u.out_edges: if (u.stage_id > v.stage_id): roots[v.stage_id].add(v) n_parts = len(parts) for (idx, group) in roots.items(): for n in find_subtree(group, len(graph.nodes)): n.stage_id = n_parts n_parts += 1
def find_subtree(roots: Set[Node], graph_size: int): nodes = set() open = copy(roots) while (len(open) > 0): n = open.pop() nodes.add(n) for u in n.out_edges: if (u.stage_id == n.stage_id): nodes.add(u) open.add(u) open = copy(nodes) while (len(open) > 0): n = open.pop() if (n in roots): continue for u in n.in_edges: if (u.stage_id == n.stage_id): if ((u.type != NodeTypes.IN) and ((n.id - u.id) > (graph_size // 2))): continue open.add(u) nodes.add(u) return nodes
def is_valid_partitioning(graph: Graph, edge_weight_function): '\n check if we only send tensors between partitions\n ' for n in graph.nodes: if (n.value_type in {type(None), list, tuple, dict, set, int, bool, float, str, slice, torch.Size, torch.dtype}): for o in n.out_edges: if (n.stage_id != o.stage_id): msg = f'invalid output type at partition boundary {n.stage_id}=>{o.stage_id}' msg += f''' output is {n.scope} of type {n.value_type}, weight {edge_weight_function(n, o)}''' return (False, msg) return (True, '')
def print_all_problematic_outputs_between_partitions(graph: Graph, edge_weight_function): '\n check if we only send tensors between partitions\n ' problems = [] valid_state = True for n in graph.nodes: if (n.value_type in {type(None), list, tuple, dict, set, int, bool, float, str, slice, torch.Size, torch.dtype}): for o in n.out_edges: if (n.stage_id != o.stage_id): msg = f'invalid output type at partition boundary {n.stage_id}=>{o.stage_id}' msg += f''' output is {n.scope} of type {n.value_type}, weight {edge_weight_function(n, o)}''' valid_state = False problems.append(msg) s = ((f'''Valid outputs states = {valid_state} ''' + 'problems:\n') + '\n'.join(problems)) print(s)
def greedy_best_fit(graph: Graph, P, node_weight_function, node_mem_estimator: NodeMemoryEstimator): bins = {i: list() for i in range(P)} bin_weights = heapdict({i: 0 for i in range(P)}) bin_memory = heapdict({i: 0 for i in range(P)}) node_to_weight = {n: node_weight_function(n) for n in graph.non_input_nodes} node_to_weight = dict(sorted(node_to_weight.items(), key=(lambda item: item[1]), reverse=True)) gpu_mem_threshold_bytes = {i: node_mem_estimator.THRESHOLD for i in bins} node_to_mem = {n: node_mem_estimator(n) for n in graph.non_input_nodes} def check_memory_fit(candidate, bin_id): if ((node_to_mem[candidate] + bin_memory[bin_id]) > gpu_mem_threshold_bytes[bin_id]): print(f'-v- failed to add candidate to GPU {bin_id}') return False return True def choose_bin(node): tmp = [] while bin_weights: (bin_id, w) = bin_weights.peekitem() if (not check_memory_fit(node, bin_id)): tmp.append(bin_weights.popitem()) continue for (i, v) in tmp: warnings.warn('it is improbable we got here.') bin_weights[i] = v return bin_id print('Could not find an assignment which fits memory') print(f'node: {node}') print('bins:') for x in tmp: print(x) print('node to mem:') pprint(node_to_mem) print(f'sum(node_to_mem.values()): {(sum(node_to_mem.values()) * 1e-09)} GB') raise RuntimeError('Could not find an assignment which fits memory') while node_to_weight: (node, node_weight) = node_to_weight.popitem() try: bin_id = choose_bin(node) except RuntimeError as e: if (sum(node_to_mem.values()) < sum(gpu_mem_threshold_bytes.values())): warnings.warn('Can find assignment using largest memory job first v1') try: bins = largest_memory_first_greedy_best_fit_v1(graph, P, node_weight_function, node_mem_estimator) return bins except Exception as ee: print(f'-v- largest_memory_first_greedy_best_fit_v1 Failed: {str(ee)}') raise e bins[bin_id].append(node) bin_weights[bin_id] += node_weight bin_memory[bin_id] += node_to_mem[node] print('bin_memory after greedy assignment:') pprint(str(bin_memory)) print(f'sum(node_to_mem.values()): {(sum(node_to_mem.values()) * 1e-09)} GB') return bins
def largest_memory_first_greedy_best_fit_v1(graph: Graph, P, node_weight_function, node_mem_estimator: NodeMemoryEstimator): bins = {i: list() for i in range(P)} bin_weights = heapdict({i: 0 for i in range(P)}) bin_memory = heapdict({i: 0 for i in range(P)}) node_to_weight = {n: node_weight_function(n) for n in graph.non_input_nodes} node_to_weight = dict(sorted(node_to_weight.items(), key=(lambda item: item[1]), reverse=True)) gpu_mem_threshold_bytes = {i: node_mem_estimator.THRESHOLD for i in bins} node_to_mem = {n: node_mem_estimator(n) for n in graph.non_input_nodes} node_to_mem = dict(sorted(node_to_mem.items(), key=(lambda item: item[1]), reverse=True)) node_to_mem_copy = {node: v for (node, v) in node_to_mem.items()} def check_memory_fit(candidate, bin_id): if ((node_to_mem[candidate] + bin_memory[bin_id]) > gpu_mem_threshold_bytes[bin_id]): print(f'-v- failed to add candidate to GPU {bin_id}') return False return True def choose_bin(node): tmp = [] while bin_weights: (bin_id, w) = bin_weights.peekitem() if (not check_memory_fit(node, bin_id)): tmp.append(bin_weights.popitem()) continue for (i, v) in tmp: warnings.warn('it is improbable we got here.') bin_weights[i] = v return bin_id print('Could not find an assignment which fits memory') print(f'node: {node}') print('bins:') for x in tmp: print(x) print('node to mem:') pprint(node_to_mem) print(f'sum(node_to_mem.values()): {(sum(node_to_mem.values()) * 1e-09)} GB') if (sum(node_to_mem.values()) < sum(gpu_mem_threshold_bytes.values())): warnings.warn('Can find assignment using largest memory job first') raise RuntimeError('Could not find an assignment which fits memory') while node_to_weight: (node, node_mem) = node_to_mem_copy.popitem() node_weight = node_to_weight.pop(node) bin_id = choose_bin(node) bins[bin_id].append(node) bin_weights[bin_id] += node_weight bin_memory[bin_id] += node_to_mem[node] print('bin_memory after greedy assignment:') pprint(str(bin_memory)) print(f'sum(node_to_mem.values()): {(sum(node_to_mem.values()) * 1e-09)} GB') return bins
def algorithm_u(ns, m): 'taken from https://codereview.stackexchange.com/questions/1526/finding-all-k-subset-partitions\n ' def visit(n, a): ps = [[] for i in range(m)] for j in range(n): ps[a[(j + 1)]].append(ns[j]) return ps def f(mu, nu, sigma, n, a): if (mu == 2): (yield visit(n, a)) else: for v in f((mu - 1), (nu - 1), ((mu + sigma) % 2), n, a): (yield v) if (nu == (mu + 1)): a[mu] = (mu - 1) (yield visit(n, a)) while (a[nu] > 0): a[nu] = (a[nu] - 1) (yield visit(n, a)) elif (nu > (mu + 1)): if (((mu + sigma) % 2) == 1): a[(nu - 1)] = (mu - 1) else: a[mu] = (mu - 1) if (((a[nu] + sigma) % 2) == 1): for v in b(mu, (nu - 1), 0, n, a): (yield v) else: for v in f(mu, (nu - 1), 0, n, a): (yield v) while (a[nu] > 0): a[nu] = (a[nu] - 1) if (((a[nu] + sigma) % 2) == 1): for v in b(mu, (nu - 1), 0, n, a): (yield v) else: for v in f(mu, (nu - 1), 0, n, a): (yield v) def b(mu, nu, sigma, n, a): if (nu == (mu + 1)): while (a[nu] < (mu - 1)): (yield visit(n, a)) a[nu] = (a[nu] + 1) (yield visit(n, a)) a[mu] = 0 elif (nu > (mu + 1)): if (((a[nu] + sigma) % 2) == 1): for v in f(mu, (nu - 1), 0, n, a): (yield v) else: for v in b(mu, (nu - 1), 0, n, a): (yield v) while (a[nu] < (mu - 1)): a[nu] = (a[nu] + 1) if (((a[nu] + sigma) % 2) == 1): for v in f(mu, (nu - 1), 0, n, a): (yield v) else: for v in b(mu, (nu - 1), 0, n, a): (yield v) if (((mu + sigma) % 2) == 1): a[(nu - 1)] = 0 else: a[mu] = 0 if (mu == 2): (yield visit(n, a)) else: for v in b((mu - 1), (nu - 1), ((mu + sigma) % 2), n, a): (yield v) n = len(ns) a = ([0] * (n + 1)) for j in range(1, (m + 1)): a[((n - m) + j)] = (j - 1) return f(m, n, 0, n, a)
def exhustive_search(graph: Graph, P, node_weight_function, node_mem_estimator: NodeMemoryEstimator, L): all_nodes = list(graph.non_input_nodes) all_weights = np.array([node_weight_function(x) for x in all_nodes]) all_mems = np.array([node_mem_estimator(x) for x in all_nodes]) L_tag = len(all_nodes) homogenous_threshold = node_mem_estimator.THRESHOLD print(f'Doing exhaustive search ') def num_stages(m): raise NotImplementedError() best_m_comp = np.inf best_solution = None for m in tqdm(algorithm_u(list(range(L_tag)), P), desc='exhustive_search'): top_mem = max((np.sum(all_mems[b]) for b in m)) if (top_mem > homogenous_threshold): continue top_comp = max((np.sum(all_weights[b]) for b in m)) if (top_comp < best_m_comp): best_m_comp = top_comp best_solution = deepcopy(m) all_nodes = np.array(all_nodes) m = best_solution bins = {i: all_nodes[b].tolist() for (i, b) in enumerate(m)} return bins
def coarsen_prefixes(model: Module, graph: Graph, node_weight_function, edge_weight_function, uf: UnionFind, basic_blocks, special_blocks, depth): prev_graph = Graph.from_other(graph) uf2 = UnionFind(elements=graph._nodes.keys()) nodes = list(graph.non_input_nodes) sb_scope_to_nodes = get_marked_nodes_for_prefix_coarsening(module=model, nodes=nodes, basic_blocks=basic_blocks, special_blocks=special_blocks, depth=depth) for (sb_scope, sb_nodes) in sb_scope_to_nodes.items(): set_sb_nodes = set(sb_nodes) sb_nodes.sort(key=(lambda n: n.topo_sort_id)) did_something = True while (did_something and (len(set_sb_nodes) > 1)): did_something = False for u in sb_nodes: if (u not in set_sb_nodes): continue for v in sorted(u.out_edges, key=(lambda n: n.topo_sort_id)): if (v not in set_sb_nodes): continue if check_cycle2(graph, u, v): continue graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(u.id, v.id) uf2.union(u.id, v.id) set_sb_nodes.discard(v) did_something = True if (len(set_sb_nodes) > 1): warnings.warn(f'failed to fully coarsen special block. remaining ({len(set_sb_nodes)}): {set_sb_nodes}') raise NotImplementedError() matching = None sb_names = list(sb_scope_to_nodes.keys()) return (prev_graph, matching, graph, uf, uf2, sb_names)
def get_marked_nodes_for_prefix_coarsening(module, nodes, basic_blocks, special_blocks, depth): sb_id_to_nodes = dict() all_sbs = [] for packed in special_traverse_model(module, depth=depth, basic_blocks=basic_blocks, special_blocks=special_blocks, full=True, mark=True): (sub_layer, scope, parent, terminal, sb_id) = packed if (sb_id is not None): all_sbs.append(packed) for packed in all_sbs: (_, scope, _, _, sb_id) = packed l = [] l = [node for node in nodes if (node.scope.startswith(scope) or (node.scope_to_hold_to and node.scope_to_hold_to.startswith(scope)))] sb_id_to_nodes[scope] = l return sb_id_to_nodes
def annotate_special_blocks_to_hold_to(model, graph, special_blocks, basic_blocks, depth): nodes = list(graph.non_input_nodes) sb_scope_to_nodes = get_marked_nodes_for_prefix_coarsening(module=model, nodes=nodes, basic_blocks=basic_blocks, special_blocks=special_blocks, depth=depth) scopes_to_hold_to = list(sb_scope_to_nodes.keys()) for node in graph.nodes: for scope_to_hold_to in scopes_to_hold_to: if node.scope.startswith(scope_to_hold_to): if ((node.scope_to_hold_to is not None) and (node.scope_to_hold_to != scope_to_hold_to)): print(f'need to assign a scope to hold to for node:{node.scope}') print(f'but node already has {node.scope_to_hold_to}') raise NotImplementedError('nested by prefix coarsening not supported') node.scope_to_hold_to = scope_to_hold_to
def stochastic_centers_matching(graph: Graph, node_weight_function: NodeWeightFunction, edge_weight_function: EdgeWeightFunction, L, P, uf: UnionFind, verbose=False, record_history=False, special_blocks=None, sb_names=None): print('stochastic_centers_matching') prev_graph = Graph.from_other(graph) uf2 = UnionFind(elements=graph._nodes.keys()) all_nodes = {n for n in graph.non_input_nodes} if (special_blocks is None): special_blocks = () bb = special_blocks sb_names = [c.__name__ for c in bb] found_nodes = {b: list() for b in sb_names} total_found = 0 for n in graph.non_input_nodes: for b in sb_names: if ((b in n.scope) or (n.scope_to_hold_to and (b in n.scope_to_hold_to))): found_nodes[b].append(n) total_found += 1 print(f'-I- Found {total_found} special blocks') pprint(found_nodes) if (total_found < L): warnings.warn(f'There are only {total_found} special blocks, but need to find {L} centers') warnings.warn('Finding {L-total_found} more random centers, all found special block centers will be centers') print('-I- assigning centers from special blocks') lengths = {b: math.floor((L * (len(nodes) / total_found))) for (b, nodes) in found_nodes.items()} total_basic_block_centers = sum(lengths.values()) print(f'-I- total_basic_block_centers: {total_basic_block_centers}') print(f'-I- centers to assign in each basic block: {lengths}') hd = deque() centers = set() to_assign = L sorted_iter = sorted(list(found_nodes.items()), key=(lambda x: len(x[1]))) for (b_name, nodes) in sorted_iter: print(f'-I- Assigning centers in block {b_name}') L_tag = len(nodes) L_prop_int = lengths[b_name] jump = math.ceil((L_tag / L_prop_int)) if (jump <= 0): continue for i in range(0, L_tag, jump): center = nodes[i] hd.append(center) centers.add(center) to_assign -= 1 if (to_assign == 0): break if (to_assign == 0): break print(f'-I- Assigned total of {len(centers)} centers:') pprint(centers) if (to_assign > 0): print(f'-I- Now, choosing {to_assign} more random centers') additional_centers = random.sample((all_nodes - centers), to_assign) for x in additional_centers: centers.add(x) hd.append(x) to_assign -= len(additional_centers) assert (to_assign == 0) print('-I- final centers:') print(hd) def inner_loop(): for i in range(len(hd)): u = hd.popleft() for v in sorted(u.out_edges, key=(lambda n: n.topo_sort_id)): if (v in centers): continue if check_cycle2(graph, u, v): continue graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(u.id, v.id) uf2.union(u.id, v.id) all_nodes.discard(v) hd.append(u) return True hd.append(u) return False history_sizes = [] history_weights = [] while (len(all_nodes) > L): merged_something = inner_loop() if (not merged_something): break if record_history: history_sizes.append((len(all_nodes) + 1)) if verbose: print(f'Nodes: {len(all_nodes)} Centers: {len(hd)}') if (len(all_nodes) > L): print(f'Merged until {len(all_nodes)} Merging more, until {L} left') def inner_loop(): for i in range(len(hd)): v = hd.popleft() v: Node for u in sorted(v.in_edges, key=(lambda n: (- n.topo_sort_id))): if (u not in all_nodes): continue if (u in centers): continue if check_cycle2(graph, u, v): continue graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(u.id, v.id) uf2.union(u.id, v.id) all_nodes.discard(v) centers.discard(v) centers.add(u) hd.append(u) return True hd.append(v) return False while (len(all_nodes) > L): merged_something = inner_loop() if (not merged_something): break if record_history: history_sizes.append((len(all_nodes) + 1)) if verbose: print(f'Nodes: {len(all_nodes)} Centers: {len(hd)}') matching = None return (prev_graph, matching, graph, uf, uf2)
def check_cycle2(g: Graph, a: Node, b: Node, nms=NodeMemoryEstimator()): '\n Checks if contracting (merging) (a,b) breaks topo order\n Args:\n g: topo-sorted graph\n a: start: first node in edge (a,b)\n b: end: second node in edge (a,b)\n\n Returns:\n True if contracting would create a cycle.\n\n ' ab = Node(None, None, 'dummy_not_None_scope') ab.out_edges = sorted((set((a.out_edges + b.out_edges)) - {a, b}), key=(lambda x: x.id)) creates_a_cycle = g.forward_dfs_and_check_if_in_set(source=ab, set_to_check={a, b}, depth_limit=None) if (not creates_a_cycle): if ((nms(a) + nms(b)) > nms.THRESHOLD): return True return creates_a_cycle
def check_cycle_given_topo_sort(g: Graph, a: Node, b: Node): '\n # TODO: Requires topological order. (e.g dyanamic topo order)\n Checks if merging (a,b) breaks topo order\n Args:\n g: topo-sorted graph\n a: start: first node in edge (a,b)\n b: end: second node in edge (a,b)\n Returns:\n True if there is another path (a->...->b) through missing nodes.\n (This means merging breaks topo order)\n ' src_ids = a.topo_sort_id dst_ids = b.topo_sort_id A = {a} B = {b} missing_ids = set(range((src_ids + 1), (dst_ids + 1))) set_inputs = set(g.inputs) missing_nodes_in_work_graph = [g[i] for i in missing_ids if ((i in g) and (g[i] not in set_inputs))] edge_nodes: Set[Node] = set(missing_nodes_in_work_graph) edges = [] for a in A: for c in a.out_edges: if (c in edge_nodes): edges.append((0, (c.topo_sort_id + 2))) for c in edge_nodes: for nc in c.out_edges: if (nc in edge_nodes): edges.append(((c.topo_sort_id + 2), (nc.topo_sort_id + 2))) elif (nc in B): edges.append(((c.topo_sort_id + 2), 1)) G = nx.DiGraph(incoming_graph_data=edges) G.add_node(0) G.add_node(1) has_path = nx.algorithms.shortest_paths.generic.has_path(G, 0, 1) is_ok = (not has_path) has_path_via_missing_nodes = (not is_ok) if (not has_path_via_missing_nodes): for nn in b.in_edges: if (nn.topo_sort_id > a.topo_sort_id): return True return has_path_via_missing_nodes
def coarsening(model, graph, edge_weight_function: EdgeWeightFunction, node_weight_function: NodeWeightFunction, L, P, basic_blocks, special_blocks, depth) -> List[Tuple[(Graph, List[List[Node]], Graph, UnionFind)]]: print(f'-I- Coarsening: got graph with {graph.num_nodes} nodes') mgr = CoarseningMgr(model, graph, edge_weight_function, node_weight_function, L, P, basic_blocks, special_blocks, depth) mgr.add_method('prefixes') mgr.add_method('forbidden_edges') mgr.add_method('node_weight_0') mgr.add_method('cco') mgr.add_method('stochastic_centers') mgr.add_method('smallest_nodes') mgr.execute() return mgr.hierarchy
class CoarseningMgr(): def __init__(self, model, graph: Graph, edge_weight_function: EdgeWeightFunction, node_weight_function: NodeWeightFunction, L, P, basic_blocks, special_blocks, depth): self.model = model self.graph = graph self.edge_weight_function = edge_weight_function self.node_weight_function = node_weight_function self.L = L self.P = P self.basic_blocks = basic_blocks self.special_blocks = special_blocks self.depth = depth print(f'-I- Coarsening: got graph with {graph.num_nodes} nodes') self.uf = UnionFind(elements=[n.id for n in graph.non_input_nodes]) self.p = graph self.pipeline = [] self.kwargs_pipeline = [] self.hierarchy = [] def add_method(self, name, *method_args, **method_kwargs): self.pipeline.append(name) self.kwargs_pipeline.append((method_args, method_kwargs)) def execute(self): if ('prefixes' in self.pipeline): annotate_special_blocks_to_hold_to(model=self.model, graph=self.graph, special_blocks=self.special_blocks, basic_blocks=self.basic_blocks, depth=self.depth) for (i, (method, (method_args, method_kwargs))) in enumerate(zip(self.pipeline, self.kwargs_pipeline)): is_last_op_in_pipe = (i == (len(self.pipeline) - 1)) if (method == 'prefixes'): self.coarsen_prefixes(is_last_op_in_pipe=is_last_op_in_pipe) elif (method == 'forbidden_edges'): self.forbidden_edges(is_last_op_in_pipe=is_last_op_in_pipe) elif (method == 'node_weight_0'): self.node_weight_0(is_last_op_in_pipe=is_last_op_in_pipe) elif (method == 'heavy_edges'): self.heavy_edges(*method_args, **method_kwargs, is_last_op_in_pipe=is_last_op_in_pipe) elif (method == 'cco'): self.cco(is_last_op_in_pipe=is_last_op_in_pipe) elif (method == 'stochastic_centers'): self.stochastic_centers(is_last_op_in_pipe=is_last_op_in_pipe) elif (method == 'smallest_nodes'): self.smallest_nodes(is_last_op_in_pipe=is_last_op_in_pipe) else: raise NotImplementedError(method) def append_to_hierarchy(self, p, uf2, g, uf, is_last_op_in_pipe=False): hierarchy = self.hierarchy if (not is_last_op_in_pipe): hierarchy.append((p, uf2, g, deepcopy(uf))) else: hierarchy.append((p, uf2, g, uf)) def coarsen_prefixes(self, is_last_op_in_pipe=False): (p, _, g, uf, uf2, sb_names) = coarsen_prefixes(model=self.model, graph=self.p, node_weight_function=self.node_weight_function, edge_weight_function=self.edge_weight_function, uf=self.uf, basic_blocks=self.basic_blocks, special_blocks=self.special_blocks, depth=self.depth) print(sb_names) print(f'merged {(len(p) - len(g))} nodes with common prefixes') self.append_to_hierarchy(p, uf2, g, uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g def forbidden_edges(self, is_last_op_in_pipe=False): matching = penalty_edges_matching(graph=self.p, edge_weight_function=self.edge_weight_function) g = contract(self.p, matching, self.edge_weight_function, uf=self.uf) print(f'merged {len(matching)} nodes with penalty edges') self.append_to_hierarchy(self.p, matching, g, self.uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g def node_weight_0(self, is_last_op_in_pipe=False): print(f'merging nodes with weight <=0') (p, _, g, uf, uf2) = nodes_leq_threshold_matching(self.p, self.node_weight_function, self.edge_weight_function, self.L, self.uf, verbose=False, record_history=True, threshold=0) self.append_to_hierarchy(p, uf2, g, self.uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g def heavy_edges(self, percentile_to_filter=0.95, is_last_op_in_pipe=False): (p, _, g, uf, uf2) = online_heavy_edge_matching(self.p, self.node_weight_function, self.edge_weight_function, self.L, self.uf, verbose=True, record_history=True, pecentile_to_filter=percentile_to_filter) self.append_to_hierarchy(p, uf2, g, self.uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g def cco(self, is_last_op_in_pipe=False): (p, _, g, uf, uf2) = systematic_comm_comp_ratio_matching(self.p, self.node_weight_function, self.edge_weight_function, self.L, self.uf, verbose=True) if (uf2 is None): warnings.warn("can't restore single step of systematic max blocks") self.append_to_hierarchy(p, uf2, g, self.uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g def stochastic_centers(self, is_last_op_in_pipe=False): (p, _, g, uf, uf2) = stochastic_centers_matching(self.p, self.node_weight_function, self.edge_weight_function, self.L, self.P, self.uf, verbose=True, record_history=False, special_blocks=self.special_blocks) self.append_to_hierarchy(p, uf2, g, self.uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g def smallest_nodes(self, is_last_op_in_pipe=False): (p, _, g, uf, uf2) = online_smallest_comp_node_matching(self.p, self.node_weight_function, self.edge_weight_function, self.L, self.uf, verbose=True, record_history=True) self.append_to_hierarchy(p, uf2, g, self.uf, is_last_op_in_pipe=is_last_op_in_pipe) self.p = g
def contract(graph: Graph, matching: List[List[Node]], edge_weight_function: EdgeWeightFunction, uf: Optional[UnionFind]=None) -> Graph: new_graph = Graph.from_other(graph) for m in sorted(matching, key=(lambda x: x[0].id), reverse=True): root = m[0] for i in m[1:]: new_graph.merge(root.id, i.id, edge_weight_function=edge_weight_function, uf=uf) if (uf is not None): uf.union(x=root.id, y=i.id) return new_graph
def penalty_edges_matching(graph: Graph, edge_weight_function: EdgeWeightFunction): "Penalized edges are for disallowing sending weird stuff which MPI and the like can't handle.\n # TODO: if this creates a cycle we have nothing to do, but manually wrap it and disallow communication of weird stuff\n " matching = [] for node in graph.non_input_nodes: check = False for out in node.out_edges: if (edge_weight_function(node, out) >= edge_weight_function.penalty): if check_cycle2(graph, node, out): warnings.warn(f"can't compress edge with penalty (node,out)={(node, out)}") continue matching.append([node, out]) check = True if check: if (not node.compound_edge_weights): try: for out in node.out_edges: assert (edge_weight_function(node, out) >= edge_weight_function.penalty) except AssertionError: for out in node.out_edges: print(edge_weight_function(node, out)) print('PENATLY', edge_weight_function.penalty) count = 0 for v in node.out_edges: if (v.id in graph.output_ids): continue count += 1 for e in matching[(- count):]: if (e[0] is not node): print('matching') for tup in matching: print(tup) print('out edges') for v in node.out_edges: print(v) raise NotImplementedError(f'potential cycle in edge {e}. (count={count}) Should probably duplicate node, or check topo order.') return matching
def code_analysis_matching(graph: Graph): pass
def adjacent_and_same_size_matching(graph: Graph): pass
def systematic_comm_comp_ratio_matching(graph: Graph, node_weight_function, edge_weight_function, L, uf: UnionFind, verbose=False): prev_graph = Graph.from_other(graph) rbc = RatioBlockCreator(graph, edge_weight_function=edge_weight_function, node_weight_function=node_weight_function, uf=uf) rbc.apply(L, verbose=verbose) matching = None return (prev_graph, matching, graph, uf, None)
def online_smallest_comp_node_matching(graph: Graph, node_weight_function, edge_weight_function, L, uf: UnionFind, verbose=False, record_history=False): prev_graph = Graph.from_other(graph) uf2 = UnionFind(elements=graph._nodes.keys()) hd = ValueSortedDict({n: node_weight_function(n) for n in graph.non_input_nodes}) def inner_loop(): for (u, weight_of_u) in hd.items(): for v in sorted(u.out_edges, key=(lambda n: node_weight_function(n))): if check_cycle2(graph, u, v): continue graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(u.id, v.id) uf2.union(u.id, v.id) hd.pop(u) hd.pop(v) hd[u] = node_weight_function(u) return (True, weight_of_u) return (False, None) history_sizes = [] history_weights = [] while (len(hd) > L): (merged_something, weight_of_u) = inner_loop() if (not merged_something): break if record_history: history_sizes.append((len(hd) + 1)) history_weights.append(weight_of_u) if verbose: print(f'Nodes: {len(hd)}, Smallest: {weight_of_u}') matching = None return (prev_graph, matching, graph, uf, uf2)
def nodes_leq_threshold_matching(graph: Graph, node_weight_function, edge_weight_function, L, uf: UnionFind, verbose=False, record_history=False, threshold=0): prev_graph = Graph.from_other(graph) uf2 = UnionFind(elements=graph._nodes.keys()) hd = ValueSortedDict({n: node_weight_function(n) for n in graph.non_input_nodes}) total_merged = 0 def inner_loop(): for (u, weight_of_u) in hd.items(): if (weight_of_u > threshold): print(f'done with nodes <= threshold {threshold}, breaking (last weight: {weight_of_u}). merged {total_merged}') return (False, None, True) u: Node for v in sorted(u.in_edges, key=(lambda n: node_weight_function(n))): if (v in graph.inputs): continue if check_cycle2(graph, v, u): continue graph.merge(uid=v.id, vid=u.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(v.id, u.id) uf2.union(v.id, u.id) hd.pop(v) hd.pop(u) hd[v] = node_weight_function(v) return (True, weight_of_u, False) for v in sorted(u.out_edges, key=(lambda n: node_weight_function(n))): if check_cycle2(graph, u, v): continue warnings.warn(f"can't merge small node {u} backward, will merge forward and lose the name of {v}.") graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(u.id, v.id) uf2.union(u.id, v.id) hd.pop(u) hd.pop(v) hd[u] = node_weight_function(u) return (True, weight_of_u, False) return (False, None, False) history_sizes = [] history_weights = [] while (len(hd) > L): (merged_something, weight_of_u, threshold_cond) = inner_loop() if threshold_cond: break if (not merged_something): break total_merged += 1 if record_history: history_sizes.append((len(hd) + 1)) history_weights.append(weight_of_u) if verbose: print(f'Nodes: {len(hd)}, Smallest: {weight_of_u}') matching = None return (prev_graph, matching, graph, uf, uf2)
def ofline_smallest_comp_node_matching(graph: Graph, node_weight_function): matching = [] matched = set() for u in sorted(graph.non_input_nodes, key=(lambda n: node_weight_function(n))): if (u in matched): continue for v in sorted(u.out_edges, key=(lambda n: node_weight_function(n))): if (v in matched): continue if check_cycle2(graph, u, v): continue matched.add(u) matched.add(v) matching.append((u, v)) return matching
def online_heavy_edge_matching(graph: Graph, node_weight_function, edge_weight_function, L, uf: UnionFind, verbose=False, record_history=False, pecentile_to_filter=0.9): prev_graph = Graph.from_other(graph) uf2 = UnionFind(elements=graph._nodes.keys()) rbc = RatioBlockCreator(graph, edge_weight_function=edge_weight_function, node_weight_function=node_weight_function, uf=uf) hd = rbc.sorted_graph_forward_edges(descending=True) def inner_loop(): for ((uid, vid), weight_of_u_v) in hd.items(): u = graph[uid] v = graph[vid] if check_cycle2(graph, u, v): continue graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf2.union(u.id, v.id) rbc.update_sorted_edges_on_merges(edges_to_value=hd, merges=[(u.id, v.id)], allow_poped_outside=True) return (True, weight_of_u_v) return (False, None) history_sizes = [] history_weights = [] import pandas as pd s = pd.Series(list(hd.values())) description = s.describe(percentiles=[0.5, 0.75, 0.8, 0.9, 0.95, 0.99]) print(description) if (pecentile_to_filter is not None): dest_length = (len(hd) * pecentile_to_filter) print(f'Filtering hte {pecentile_to_filter} percentile') else: dest_length = L while (len(hd) > dest_length): (merged_something, weight_of_merged) = inner_loop() if (not merged_something): break if record_history: history_sizes.append((len(hd) + 1)) history_weights.append(weight_of_merged) if verbose: print(f'Edges: {len(hd)}, Largest edge: {weight_of_merged}') matching = None return (prev_graph, matching, graph, uf, uf2)
def full_alg(graph, P, L, node_weight_function, edge_weight_function, uf, rtol=0.002): history = get_rep_analysis_history_with_online_smallest_comp_node_matching(graph, node_weight_function=node_weight_function, edge_weight_function=edge_weight_function, L=L, uf=uf, rtol=rtol, verbose=False) torch.save(history, 'history.tmp') print('Saved history to file history.tmp') repetitive_adjacent_analysis(history, L, P)
def repetitive_adjacent_analysis(history: List[List[Set[Node]]], L, P): for (i, found_sets) in enumerate(history): lengths = [len(x) for x in found_sets] print(f'-I- merge {i} Found set lengths {lengths}') for l in lengths: if ((l % P) == 0): k = (l // P) print(f' Found set of size {l} splitting it to {k}*{P} groups') elif (l > P): print(f' Found set of size {l}, currently ignoring')
def record_repetitive_adjacent(graph, node_weight_function, rtol=0.002, do_topo_sort=True): if do_topo_sort: graph.topo_sort(change_graph=False) topo_sorted_nodes_to_weight = SortedDict({n.topo_sort_id: node_weight_function(n) for n in graph.non_input_nodes}) found_sets = [] cur = None rsum = 0 cur_set = set() for (node, weight) in topo_sorted_nodes_to_weight.items(): if (cur is None): cur = weight cur_set.add(node) rsum = weight elif np.allclose(weight, cur, rtol): rsum += weight cur_set.add(node) cur = (rsum / len(cur_set)) else: if cur_set: found_sets.append(cur_set) cur = weight rsum = weight cur_set = set() return found_sets
def get_rep_analysis_history_with_online_smallest_comp_node_matching(graph: Graph, node_weight_function, edge_weight_function, L, uf: UnionFind, verbose=True, rtol=0.002): prev_graph = Graph.from_other(graph) (graph, prev_graph) = (prev_graph, graph) uf = deepcopy(uf) hd = ValueSortedDict({n: node_weight_function(n) for n in graph.non_input_nodes}) def inner_loop(): for (u, weight_of_u) in hd.items(): for v in sorted(u.out_edges, key=(lambda n: node_weight_function(n))): if check_cycle2(graph, u, v): continue graph.merge(uid=u.id, vid=v.id, edge_weight_function=edge_weight_function, uf=uf) uf.union(u.id, v.id) hd.pop(u) hd.pop(v) hd[u] = node_weight_function(u) return (True, weight_of_u) return (False, None) rep_analysis_history = [] while (len(hd) > L): (merged_something, weight_of_u) = inner_loop() if (not merged_something): break found_sets = record_repetitive_adjacent(graph, node_weight_function, rtol=rtol, do_topo_sort=True) rep_analysis_history.append(found_sets) if verbose: print(f'Nodes: {len(hd)}, Smallest: {weight_of_u}') return rep_analysis_history
def doc(s): if hasattr(s, '__call__'): s = s.__doc__ def f(g): g.__doc__ = s return g return f
class heapdict(MutableMapping): __marker = object() def __init__(self, *args, **kw): self.heap = [] self.d = {} self.update(*args, **kw) @doc(dict.clear) def clear(self): del self.heap[:] self.d.clear() @doc(dict.__setitem__) def __setitem__(self, key, value): if (key in self.d): self.pop(key) wrapper = [value, key, len(self)] self.d[key] = wrapper self.heap.append(wrapper) self._decrease_key((len(self.heap) - 1)) def _min_heapify(self, i): n = len(self.heap) h = self.heap while True: l = ((i << 1) + 1) r = ((i + 1) << 1) if ((l < n) and (h[l][0] < h[i][0])): low = l else: low = i if ((r < n) and (h[r][0] < h[low][0])): low = r if (low == i): break self._swap(i, low) i = low def _decrease_key(self, i): while i: parent = ((i - 1) >> 1) if (self.heap[parent][0] < self.heap[i][0]): break self._swap(i, parent) i = parent def _swap(self, i, j): h = self.heap (h[i], h[j]) = (h[j], h[i]) h[i][2] = i h[j][2] = j @doc(dict.__delitem__) def __delitem__(self, key): wrapper = self.d[key] while wrapper[2]: parentpos = ((wrapper[2] - 1) >> 1) parent = self.heap[parentpos] self._swap(wrapper[2], parent[2]) self.popitem() @doc(dict.__getitem__) def __getitem__(self, key): return self.d[key][0] @doc(dict.__iter__) def __iter__(self): return iter(self.d) def popitem(self): 'D.popitem() -> (k, v), remove and return the (key, value) pair with lowest\nvalue; but raise KeyError if D is empty.' wrapper = self.heap[0] if (len(self.heap) == 1): self.heap.pop() else: self.heap[0] = self.heap.pop() self.heap[0][2] = 0 self._min_heapify(0) del self.d[wrapper[1]] return (wrapper[1], wrapper[0]) @doc(dict.__len__) def __len__(self): return len(self.d) def peekitem(self): 'D.peekitem() -> (k, v), return the (key, value) pair with lowest value;\n but raise KeyError if D is empty.' return (self.heap[0][1], self.heap[0][0]) def __str__(self): return str(self.d)
class ReminderPolicy(Enum): ToLast = 'last' ToMin = 'min'
class SecondAndOnClusterPolicy(Enum): BestFitBinPacking = 'best_fit' InOrder = 'order' Reversed = 'reversed'
def maketree(n, iterable): d = deque(iterable) res = [] while d: pair = [d.popleft() for _ in range(n)] res.append(pair) return res
def flatten_subsplit(subsplit): to_add = [] for i in subsplit: if isinstance(i, list): to_add.extend(i) else: to_add.append(i) return to_add
def sum_subsplit_weight(subsplit): return sum((i.weight for i in flatten_subsplit(subsplit)))
def get_all_splits(K: int, clusters, id_to_node: Dict[(int, Node)], to_unify: Dict[(int, List[Union[(List, Any)]])], C: int, reminder_policy: ReminderPolicy=ReminderPolicy.ToLast): all_splits = [] assert (len(clusters.cluster.unique()) == C) clusters = [list(clusters.groupby('cluster').get_group(c).sort_values('id').itertuples()) for c in range(C)] clusters_lengths = {i: len(clusters[i]) for i in range(len(clusters))} print('cluster_lengths, before compressing', clusters_lengths) new_clusters = get_unified_clusters(clusters, to_unify) clusters = new_clusters clusters_lengths = {i: len(clusters[i]) for i in range(len(clusters))} print('cluster_lengths, after compressing', clusters_lengths) for (c_i, cluster) in enumerate(clusters): n_i = len(cluster) reminder = (n_i % K) only_reminder = False if (n_i < K): only_reminder = True warnings.warn(f'small number of items in cluster {c_i}: {n_i} need at least {K}. will treat as reminder with policy {reminder_policy}') N = (n_i // K) if (not only_reminder): cluster_for_split = (cluster if (not reminder) else cluster[:(- reminder)]) split = list(maketree(n=N, iterable=cluster_for_split)) else: cluster_for_split = cluster split = [[x] for x in cluster_for_split] reminder = 0 if (reminder > 0): if (reminder_policy == ReminderPolicy.ToLast): warnings.warn(f'cluster {c_i} is problematic, {n_i}%{K}!=0, will put reminding {reminder} nodes in last partition') split[(- 1)].extend(cluster[(- reminder):]) elif (reminder_policy == ReminderPolicy.ToMin): warnings.warn(f'cluster {c_i} is problematic {c_i}, {n_i}%{K}!=0, will put reminding {reminder} nodes in min weight partition') min_idx = np.argmin([sum_subsplit_weight(subsplit) for subsplit in split]) split[min_idx].extend(cluster[(- reminder):]) else: raise NotImplementedError(f'reminder_policy:{reminder_policy}') all_splits.append(split) return all_splits
def get_unified_clusters(clusters, to_unify): def to_set(v, s): if (not isinstance(v, list)): s.add(v) return for x in v: to_set(x, s) (A, B) = (set(), set()) to_set(clusters, A) new_clusters = [] for (c_i, cluster) in enumerate(clusters): to_unify_for_cluster = to_unify[c_i] cluster_D = {i.Index: i for i in cluster} deleted_from_cluster = {} next_gen = [] first_time = True while (first_time or next_gen): first_time = False if next_gen: to_unify_for_cluster = next_gen next_gen = [] for l in to_unify_for_cluster: z = l[0] x = l[1] if isinstance(cluster_D[x], list): v = cluster_D[x] zz = cluster_D[z] if isinstance(zz, list): v.extend(zz) else: v.append(zz) v.sort(key=(lambda y: y.Index)) else: v = [cluster_D[x]] try: zz = cluster_D[z] except KeyError as e: if (not (z in deleted_from_cluster)): raise e else: warnings.warn(f'found a double: {l}, I already deleted {z} and unified it with {deleted_from_cluster[z]}, will unify now to {x}') next_gen.append(sorted([x, deleted_from_cluster[z]])) continue if isinstance(zz, list): v.extend(zz) else: v.append(zz) v.sort(key=(lambda y: y.Index)) cluster_D[x] = v deleted_from_cluster[z] = x del cluster_D[z] cluster = [] for i in sorted(cluster_D.keys()): cluster.append(cluster_D[i]) new_clusters.append(cluster) to_set(new_clusters, B) assert (A == B), (A, B) return new_clusters
def make_clusters(graph: Graph, nodes: List[Node], node_weight_function, C: int, THRESHOLD=0): def node_to_record(node): return {'id': node.id, 'weight': node_weight_function(node)} records = [node_to_record(node) for node in nodes] X = pd.DataFrame.from_records(data=records, index='id') nodes_below_thresholds = X[(X['weight'] <= THRESHOLD)] nodes_above_thresholds = X[(X['weight'] > THRESHOLD)] kmeans = KMeans(n_clusters=C, max_iter=1000, copy_x=True).fit(nodes_above_thresholds) X.loc[(nodes_above_thresholds.index, 'cluster')] = kmeans.labels_ to_unify = defaultdict(list) set_idx = set(nodes_below_thresholds.index) def _basic_nest_forward(y: Node, X, set_idx, node_id, to_unify, nesting_to_take=0, curr_nesting=0): for y in y.out_edges: if (curr_nesting == nesting_to_take): if (y.id not in set_idx): dst_cluster = X.loc[y.id]['cluster'] X.loc[((X.index == node_id), 'cluster')] = dst_cluster to_unify[dst_cluster].append([node_id, y.id]) print(f'-V- unify node: {node.id} to dst: {y.id}, cluster: {dst_cluster} (forward)') return True else: return _basic_nest_forward(y, X, set_idx, node_id, to_unify, nesting_to_take=nesting_to_take, curr_nesting=(curr_nesting + 1)) return False def _basic_nest_backward(y: Node, X, set_idx, node_id, to_unify, nesting_to_take=0, curr_nesting=0): for y in y.in_edges: if (curr_nesting == nesting_to_take): if (y.id not in set_idx): try: dst_cluster = X.loc[y.id]['cluster'] except KeyError: continue X.loc[((X.index == node_id), 'cluster')] = dst_cluster to_unify[dst_cluster].append([y.id, node_id]) print(f'-V- unify node: {node.id} to dst: {y.id}, cluster: {dst_cluster} (backward)') return True else: return _basic_nest_backward(y, X, set_idx, node_id, to_unify, nesting_to_take=nesting_to_take, curr_nesting=(curr_nesting + 1)) return False for node_id in nodes_below_thresholds.index: node = graph[node_id] nesting_to_take = 0 NESTING_LIMIT = (len(graph) + 1) while True: broke = (_basic_nest_forward(node, X, set_idx, node_id, to_unify, nesting_to_take=nesting_to_take, curr_nesting=0) or _basic_nest_backward(node, X, set_idx, node_id, to_unify, nesting_to_take=nesting_to_take, curr_nesting=0)) if broke: break nesting_to_take += 1 print(f'Going {(nesting_to_take + 1)} more nesting level for node:{node_id} because all outputs are below threshold {set_idx}') if (nesting_to_take >= NESTING_LIMIT): raise NotImplementedError(f'did not find node with above THRESHOLD={THRESHOLD} weight to unify') for n in graph.nodes: n.out_edges.sort(key=(lambda x: x.id)) cluster_to_min_node_id = {i: X.query(f'cluster == {i}').first_valid_index() for i in range(C)} min_node_id_to_cluster = {v: i for (i, v) in cluster_to_min_node_id.items()} Y = X.copy() for (i, (min_node_id, cluster_id)) in enumerate(min_node_id_to_cluster.items()): Y.loc[((X['cluster'] == cluster_id), 'cluster')] = i X = Y print(X) Y = X.copy() Y['scope'] = [node.scope for node in nodes] print(Y) cluster_sums = X.groupby('cluster')['weight'].describe().transpose() print('cluster_sums_statistics', cluster_sums) clusters = X return (clusters, to_unify)
def best_Fit_cluster(K: int, clusters, id_to_node: Dict[(int, Node)], to_unify: Dict[(int, List[Union[(List, Any)]])], C: int, second_and_on_cluster_policy: SecondAndOnClusterPolicy=SecondAndOnClusterPolicy.BestFitBinPacking, reminder_policy: ReminderPolicy=ReminderPolicy.ToLast): bins = defaultdict(list) bin_weights = heapdict({i: 0 for i in range(K)}) bin_memory = heapdict({i: 0 for i in range(K)}) all_splits = get_all_splits(K, clusters, id_to_node=id_to_node, to_unify=to_unify, C=C, reminder_policy=reminder_policy) def check_memory_fit(candidate, bin_id): return True def choose_bin(subsplit, subsplit_idx, cluster_idx): if ((cluster_idx == 0) and (subsplit_idx >= K)): warnings.warn(f'not fully implemented behavior for 1st cluster subsplit_idx >= K (subsplit_idx:{subsplit_idx},K:{K}), will do FirstFitBinPacking') if ((cluster_idx == 0) and (subsplit_idx < K)): return subsplit_idx elif ((second_and_on_cluster_policy == SecondAndOnClusterPolicy.BestFitBinPacking) or ((cluster_idx == 0) and (subsplit_idx >= K))): saved = [] while True: if (len(bin_weights) == 0): raise RuntimeError('no bin can fit (memory-wise)') (emptiest_bin_id, current_bin_weight) = bin_weights.peekitem() fits_memory = check_memory_fit(subsplit, emptiest_bin_id) if fits_memory: break saved.append(bin_weights.popitem()) for (k, v) in saved: bin_weights[k] = v return emptiest_bin_id elif (second_and_on_cluster_policy == SecondAndOnClusterPolicy.InOrder): if (subsplit_idx < K): return subsplit_idx else: raise NotImplementedError('probably 1st cluster >= K came here') elif (second_and_on_cluster_policy == SecondAndOnClusterPolicy.Reversed): if (subsplit_idx < K): if ((cluster_idx % 2) != 0): return ((K - subsplit_idx) - 1) else: return subsplit_idx else: raise NotImplementedError('probably 1st cluster >= K came here') for (cluster_idx, split) in enumerate(reversed(all_splits)): if ((len(split) > K) and (cluster_idx == 0)): raise NotImplementedError() if ((len(split) < K) and (cluster_idx == 0)): warnings.warn(f'got only reminder in 1st and largest cluster: {split}') if ((cluster_idx > 0) and (second_and_on_cluster_policy == SecondAndOnClusterPolicy.BestFitBinPacking)): split = sorted(split, key=sum_subsplit_weight, reverse=True) for (subsplit_idx, subsplit) in enumerate(split): bin_idx = choose_bin(subsplit, subsplit_idx, cluster_idx) bin = bins[bin_idx] to_add = flatten_subsplit(subsplit) bin.extend(to_add) bin_weights[bin_idx] += sum((i.weight for i in to_add)) assert (len(bins) == K) return bins
def stages_from_bins(graph: Graph, bins: Dict[(int, List[Node])], id_to_node_worked_on: Dict[(int, Node)], verbose=False, assert_missing_in_bins=False, convert_id_to_node_to_topo=False): if convert_id_to_node_to_topo: tmp = dict() for (i, v) in id_to_node_worked_on.items(): tmp[v.topo_sort_id] = v id_to_node_worked_on = tmp del tmp bins_to_id = {p: set((n.topo_sort_id for n in v if (n.topo_sort_id in id_to_node_worked_on))) for (p, v) in bins.items()} nodes_with_out_edges_to_different_gpu = defaultdict(set) nodes_with_in_edges_from_different_gpu = defaultdict(set) all_broken_stages = [] for (gpu_id, nodes_in_bin) in bins.items(): unbroken_stages = get_ccs_on_same_gpu(bins_to_id, gpu_id, nodes_in_bin, nodes_with_in_edges_from_different_gpu, nodes_with_out_edges_to_different_gpu) broken_stages = break_ccs_on_same_gpu_to_stages(graph, id_to_node_worked_on, unbroken_stages, bins_to_id, assert_missing_in_bins=assert_missing_in_bins) if verbose: print('unbroken_stages') print(unbroken_stages) print('broken_stages') print(broken_stages) broken_stages: List[List[int]] all_broken_stages.extend(broken_stages) all_broken_stages.sort(key=(lambda topo_sorted_list: topo_sorted_list[0])) for (i, topo_sorted_list) in enumerate(all_broken_stages): for nid in topo_sorted_list: n = id_to_node_worked_on[nid] n.stage_id = i return len(all_broken_stages)
def break_ccs_on_same_gpu_to_stages(graph, id_to_node_worked_on, unbroken_stages, bins_to_id, assert_missing_in_bins=False): broken_stages = [] for unbroken_stage in unbroken_stages: broken_stages_for_unbroken_stage = [] cur_set = list() unbroken_stage = deque(sorted(unbroken_stage)) while unbroken_stage: prev_topo_sort_id = unbroken_stage.popleft() if (prev_topo_sort_id in id_to_node_worked_on): cur_set.append(prev_topo_sort_id) break else: print(f'skipping input_v0: {prev_topo_sort_id}') while unbroken_stage: topo_sort_id = unbroken_stage.popleft() if (topo_sort_id == (prev_topo_sort_id + 1)): pass elif (topo_sort_id not in id_to_node_worked_on): print(f'skipping input_v1: {prev_topo_sort_id}') else: has_path_via_missing_nodes = ccs_on_same_gpu_has_path_via_missing_nodes(cur_set, graph, id_to_node_worked_on, prev_topo_sort_id, topo_sort_id, unbroken_stage) if has_path_via_missing_nodes: broken_stages_for_unbroken_stage.append(cur_set) cur_set = list() if assert_missing_in_bins: missing_topo_sort_ids = list(range((prev_topo_sort_id + 1), topo_sort_id)) for mid in missing_topo_sort_ids: in_bins = any(map((lambda v: (mid in v)), bins_to_id.values())) if (not in_bins): print(f'missing_topo_sort_ids are not in bins {missing_topo_sort_ids}') raise ValueError(f'missing_topo_sort_ids are not in bins {missing_topo_sort_ids}') if (topo_sort_id in id_to_node_worked_on): cur_set.append(topo_sort_id) prev_topo_sort_id = topo_sort_id else: print(f'skipping input_v2: {prev_topo_sort_id}') while unbroken_stage: prev_topo_sort_id = unbroken_stage.popleft() if (prev_topo_sort_id in id_to_node_worked_on): cur_set.append(prev_topo_sort_id) break else: print(f'skipping input_v3: {prev_topo_sort_id}') if cur_set: broken_stages_for_unbroken_stage.append(cur_set) broken_stages.extend(broken_stages_for_unbroken_stage) broken_stages.sort(key=(lambda topo_sorted_list: topo_sorted_list[0])) return broken_stages
def ccs_on_same_gpu_has_path_via_missing_nodes(cur_set, graph, id_to_node_worked_on, prev_topo_sort_id, topo_sort_id, unbroken_stage): missing_topo_sort_ids = list(range((prev_topo_sort_id + 1), topo_sort_id)) is_ok = True for missing_topo_sort_id in missing_topo_sort_ids: if (missing_topo_sort_id not in id_to_node_worked_on): continue if (id_to_node_worked_on[missing_topo_sort_id].id not in graph): continue cur_nodes = [id_to_node_worked_on[x] for x in cur_set] scs = set(cur_set) missing_nodes_in_work_graph = [id_to_node_worked_on[x] for x in missing_topo_sort_ids if ((x not in scs) and (x in id_to_node_worked_on))] nodes_left_in_unborken_stage = set((id_to_node_worked_on[x] for x in unbroken_stage)) nodes_left_in_unborken_stage.add(id_to_node_worked_on[topo_sort_id]) A: Set[Node] = set(cur_nodes) B: Set[Node] = set(nodes_left_in_unborken_stage) edge_nodes: Set[Node] = set(missing_nodes_in_work_graph) edges = [] for a in A: for c in a.out_edges: if (c in edge_nodes): edges.append((0, (c.id + 2))) for c in edge_nodes: for nc in c.out_edges: if (nc in edge_nodes): edges.append(((c.id + 2), (nc.id + 2))) elif (nc in B): edges.append(((c.id + 2), 1)) G = nx.DiGraph(incoming_graph_data=edges) G.add_node(0) G.add_node(1) has_path = nx.algorithms.shortest_paths.generic.has_path(G, 0, 1) is_ok = (not has_path) if (not is_ok): break has_path_via_missing_nodes = (not is_ok) return has_path_via_missing_nodes
def get_ccs_on_same_gpu(bins_to_id, gpu_id, nodes_in_bin, nodes_with_in_edges_from_different_gpu, nodes_with_out_edges_to_different_gpu): uf = UnionFind(elements=bins_to_id[gpu_id]) open = deque(sorted(nodes_in_bin, key=(lambda x: x.topo_sort_id))) while open: x = open.popleft() x: Node for y in x.out_edges: if (y.topo_sort_id not in uf): nodes_with_out_edges_to_different_gpu[gpu_id].add(x) nodes_with_in_edges_from_different_gpu[y.gpu_id].add(y) continue uf.union(x.topo_sort_id, y.topo_sort_id) unbroken_stages = uf.sorted_components() return unbroken_stages
def analyze_n_clusters(nodes: List[Node], node_weight_function, max_k=10, THRESHOLD=0, manual_choose_n_clusters=True): ' utility to help determine number of clusters for partition_2dbin_pack' def node_to_record(node): return {'id': node.id, 'weight': node_weight_function(node)} records = [node_to_record(node) for node in nodes] records = [node_to_record(node) for node in nodes] X = pd.DataFrame.from_records(data=records, index='id') nodes_below_thresholds = X[(X['weight'] <= THRESHOLD)] nodes_above_thresholds = X[(X['weight'] > THRESHOLD)] X = pd.DataFrame.from_records(data=records, index='id') print(X) Y = X.copy() Y['scope'] = [node.scope for node in nodes] print(Y) sse = {} for k in range(1, (max_k + 1)): kmeans = KMeans(n_clusters=k, max_iter=1000, copy_x=True).fit(nodes_above_thresholds) X.loc[(nodes_above_thresholds.index, 'cluster')] = kmeans.labels_ sse[k] = kmeans.inertia_ plt.figure() plt.plot(list(sse.keys()), list(sse.values())) plt.xlabel('Number of clusters') plt.ylabel('SSE') plt.show(block=False) if manual_choose_n_clusters: n_clusters = input('-I- choose desired number of clusters to continue...') n_clusters = int(n_clusters) return n_clusters
def partition_2dbin_pack(graph: Graph, num_gpus: int, n_clusters: int, node_weight_function: Optional[NodeWeightFunction]=None, use_layers_graph: bool=True, THRESHOLD=0, second_and_on_cluster_policy: SecondAndOnClusterPolicy=SecondAndOnClusterPolicy.BestFitBinPacking, reminder_policy: ReminderPolicy=ReminderPolicy.ToLast, display_cluster_sse_plot=False, **kwargs): if isinstance(second_and_on_cluster_policy, type(next(iter(ReminderPolicy._value2member_map_.keys())))): second_and_on_cluster_policy = SecondAndOnClusterPolicy._value2member_map_[second_and_on_cluster_policy] if isinstance(reminder_policy, type(next(iter(ReminderPolicy._value2member_map_.keys())))): reminder_policy = ReminderPolicy._value2member_map_[reminder_policy] graph.topo_sort() if use_layers_graph: (work_graph, lookup) = graph.new_graph_without_constants() else: (work_graph, lookup) = (graph, None) nodes = [n for n in work_graph.nodes if (n not in work_graph.inputs)] K = num_gpus if (('analyze_n_clusters' in kwargs) and kwargs['analyze_n_clusters']): n_clusters = analyze_n_clusters(nodes, node_weight_function, max_k=10, THRESHOLD=THRESHOLD, manual_choose_n_clusters=True) print(f'-I- Will use n_clusters={n_clusters}') elif display_cluster_sse_plot: print('-V- displaying info about n_clusters') analyze_n_clusters(nodes, node_weight_function, max_k=10, THRESHOLD=THRESHOLD, manual_choose_n_clusters=False) id_to_node = {node.id: node for node in nodes} C = n_clusters (clusters, to_unify) = make_clusters(work_graph, nodes, node_weight_function, C=C, THRESHOLD=THRESHOLD) bins = best_Fit_cluster(K, clusters, id_to_node=id_to_node, to_unify=to_unify, C=C, second_and_on_cluster_policy=second_and_on_cluster_policy, reminder_policy=reminder_policy) for v in bins.values(): v.sort(key=(lambda x: x.Index)) pprint(bins) def node_list(iterable): return [id_to_node[i.Index] for i in iterable] bins = {i: node_list(bins[i]) for i in bins} times = {i: sum((node_weight_function(x) for x in bins[i])) for i in bins} print('times:') pprint(times) for (i, bin_nodes) in bins.items(): for n in bin_nodes: n.gpu_id = i work_graph.topo_sort(change_graph=False) stages_from_bins(work_graph, bins, id_to_node_worked_on=id_to_node, convert_id_to_node_to_topo=True) work_graph = post_process_partition(work_graph) if use_layers_graph: graph.induce_layer_partition(work_graph, lookup) stage_to_gpu_map = convert_handle_missing_print(bins, graph) return (graph, stage_to_gpu_map)