coloring

app.py

@@ -3,6 +3,21 @@ import graphviz
 import random
 import gurobipy as gp
 from gurobipy import GRB
+import colorsys 
+ 
+
+def hsv2rgb(h, s, v): 
+    r, g, b = colorsys.hsv_to_rgb(h, s, v) 
+    return int(255 * r), int(255 * g), int(255 * b)
+ 
+
+def format_color(color): 
+    return '#%02x%02x%02x' % color
+
+
+def generate_colors(n): 
+    colors = [hsv2rgb(i / n, 0.5, 1.0) for i in range(n)]
+    return [format_color(color) for color in colors]
 
 
 def generate_random_graph(V, density):
@@ -15,42 +30,30 @@ def generate_random_graph(V, density):
 def solve_matching(V, E):
     m = gp.Model()
     x = m.addVars(E, vtype=GRB.BINARY)
-    
     m.setObjective(x.sum(), GRB.MAXIMIZE)
     m.addConstrs(x.sum(u, '*') + x.sum('*', u) <= 1 for u in range(V))
-    
     m.optimize()
-    
-    matching = []
-    for e in E:
-        if x[e].x > 0.5:
-            matching.append(e)
-
-    return matching
+    return [e for e in E if x[e].x > 0.5]
 
 
 def app_matching(V, E):
     M = set(solve_matching(V, E))
-
     if len(M) == V // 2:
         st.success('Perfect matching found')
     else:
         st.metric('Matching size', len(M))
-
     G = graphviz.Graph()
     for u, v in E:
         if (u, v) in M:
             G.edge(str(u), str(v), color='red')
         else:
             G.edge(str(u), str(v), color='gray', style='dashed')
-
     st.graphviz_chart(G)
 
 
 def solve_hamilton(V, E):
     m = gp.Model()
     x = m.addVars(range(V), range(V), vtype=GRB.BINARY)
-
     m.addConstrs(x.sum(u, '*') == 1 for u in range(V))
     m.addConstrs(x.sum('*', i) == 1 for i in range(V))
     for u in range(V):
@@ -59,12 +62,9 @@ def solve_hamilton(V, E):
                 for i in range(V - 1):
                     m.addConstr(x[u, i] + x[v, i + 1] <= 1)
                 m.addConstr(x[u, V - 1] + x[v, 0] <= 1)
-
     m.optimize()
-
     if m.status != GRB.OPTIMAL:
         return None
-    
     cycle = []
     for i in range(V):
         for u in range(V):
@@ -76,12 +76,10 @@ def solve_hamilton(V, E):
 
 def app_hamilton(V, E):
     cycle = solve_hamilton(V, E)
-
     if cycle is None:
         st.error('Hamilton cycle not found')
     else:
         st.success('Hamilton cycle found')
-
     G = graphviz.Graph()
     if cycle is not None:
         for u in range(V):
@@ -98,7 +96,6 @@ def app_hamilton(V, E):
             G.node(str(u))
         for u, v in E:
             G.edge(str(u), str(v))
-
     st.graphviz_chart(G)
 
 
@@ -125,6 +122,31 @@ def app_vertex_cover(V, E):
     st.graphviz_chart(G)
 
 
+def solve_coloring(V, E):
+    m = gp.Model()
+    vertex_color = m.addVars(range(V), vtype=GRB.INTEGER, lb=0)
+    or_helper = m.addVars(E, vtype=GRB.BINARY)
+    chi = m.addVar(vtype=GRB.INTEGER)
+    m.setObjective(chi, GRB.MINIMIZE)
+    m.addConstrs(vertex_color[u] <= chi for u in range(V))
+    m.addConstrs((or_helper[u, v] == 0) >> (vertex_color[u] - vertex_color[v] >= 1) for u, v in E)
+    m.addConstrs((or_helper[u, v] == 1) >> (vertex_color[v] - vertex_color[u] >= 1) for u, v in E)
+    m.optimize()
+    return [round(vertex_color[u].x) for u in range(V)]
+
+
+def app_coloring(V, E):
+    coloring = solve_coloring(V, E)
+    st.metric('Chromatic number', max(coloring) + 1)
+    colors = generate_colors(max(coloring) + 1)
+    G = graphviz.Graph()
+    for u in range(V):
+        G.node(str(u), style='filled', fillcolor=colors[coloring[u]])
+    for u, v in E:
+        G.edge(str(u), str(v))
+    st.graphviz_chart(G)
+
+
 def main():
     V = st.number_input('Number of vertices', min_value=1, value=10)
     density = st.slider('Density', min_value=0.0, max_value=1.0, value=0.5)
@@ -140,12 +162,14 @@ def main():
         app_matching,
         app_hamilton,
         app_vertex_cover,
+        app_coloring,
     ]
 
     tabs = st.tabs([
         'Matching',
         'Hamilton',
         'Vertex cover',
+        'Coloring',
     ])
 
     for t, a in zip(tabs, apps):