Added vertex-limited network flow reduction

networking_flow/vertex_limited.py

@@ -0,0 +1,48 @@
+from networking_flow.ford_fulkerson import ford_fulkerson
+
+# Max-Flow reduction for vertex-limited networks (rather than edge-limited)
+"""
+Reduces a network that has vertex capacities into a network with edge capacities
+so that Ford-Fulkerson will work.
+Explanation: https://en.wikipedia.org/wiki/Maximum_flow_problem#Maximum_flow_with_vertex_capacities
+"""
+
+
+def vertex_limited(graph, limits):
+    max_flow_graph = [[0 for i in range(2 * len(graph))] for j in range(2 * len(graph))]
+
+    # Give all directed edges infinite capacity
+    for src_vertex in range(len(graph)):
+        for dest_vertex in range(len(graph[0])):
+            if graph[src_vertex][dest_vertex] == 1:
+                max_flow_graph[src_vertex][dest_vertex] = float("inf")
+
+    # Expand all vertices into two vertices
+    for src_vertex in range(len(graph)):
+        # move all outbound edges of the vertex to the new vertex
+        max_flow_graph[src_vertex + len(graph)] = max_flow_graph[src_vertex]
+        max_flow_graph[src_vertex] = [0 for i in range(len(max_flow_graph))]
+
+        # create edge with capacity equal to the vertex's limit
+        # from the original vertex to the new vertex
+        max_flow_graph[src_vertex][src_vertex + len(graph)] = limits[src_vertex]
+
+    return max_flow_graph
+
+
+# Test Case
+
+
+limits = [29, 12, 14, 20, 7, 29]
+graph = [  # rows are source, columns are destination
+    [0, 1, 1, 0, 0, 0],
+    [0, 0, 1, 1, 0, 0],
+    [0, 1, 0, 0, 1, 0],
+    [0, 0, 1, 0, 0, 1],
+    [0, 0, 0, 1, 0, 1],
+    [0, 0, 0, 0, 0, 0],
+]
+
+mf_graph = vertex_limited(graph, limits)
+print(mf_graph)  # prints graph reduced to a standard flow network
+print(ford_fulkerson(mf_graph, 0, len(mf_graph) - 1))  # max flow should be 19