| /* | |
| * bipartite_match.h | |
| * | |
| * Copyright (c) 2015-2023, PostgreSQL Global Development Group | |
| * | |
| * src/include/lib/bipartite_match.h | |
| */ | |
| /* | |
| * Given a bipartite graph consisting of nodes U numbered 1..nU, nodes V | |
| * numbered 1..nV, and an adjacency map of undirected edges in the form | |
| * adjacency[u] = [k, v1, v2, v3, ... vk], we wish to find a "maximum | |
| * cardinality matching", which is defined as follows: a matching is a subset | |
| * of the original edges such that no node has more than one edge, and a | |
| * matching has maximum cardinality if there exists no other matching with a | |
| * greater number of edges. | |
| * | |
| * This matching has various applications in graph theory, but the motivating | |
| * example here is Dilworth's theorem: a partially-ordered set can be divided | |
| * into the minimum number of chains (i.e. subsets X where x1 < x2 < x3 ...) by | |
| * a bipartite graph construction. This gives us a polynomial-time solution to | |
| * the problem of planning a collection of grouping sets with the provably | |
| * minimal number of sort operations. | |
| */ | |
| typedef struct BipartiteMatchState | |
| { | |
| /* inputs: */ | |
| int u_size; /* size of U */ | |
| int v_size; /* size of V */ | |
| short **adjacency; /* adjacency[u] = [k, v1,v2,v3,...,vk] */ | |
| /* outputs: */ | |
| int matching; /* number of edges in matching */ | |
| short *pair_uv; /* pair_uv[u] -> v */ | |
| short *pair_vu; /* pair_vu[v] -> u */ | |
| /* private state for matching algorithm: */ | |
| short *distance; /* distance[u] */ | |
| short *queue; /* queue storage for breadth search */ | |
| } BipartiteMatchState; | |
| extern BipartiteMatchState *BipartiteMatch(int u_size, int v_size, short **adjacency); | |
| extern void BipartiteMatchFree(BipartiteMatchState *state); | |