Hopcroft–Karp algorithm in Python

Posted by Simon on Stack Overflow See other posts from Stack Overflow or by Simon
Published on 2011-01-15T00:11:09Z Indexed on 2011/01/15 4:53 UTC
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I am trying to implement the Hopcroft Karp algorithm in Python using networkx as graph representation.

Currently I am as far as this:

#Algorithms for bipartite graphs

import networkx as nx
import collections

class HopcroftKarp(object):
    INFINITY = -1

    def __init__(self, G):
        self.G = G

    def match(self):
        self.N1, self.N2 = self.partition()
        self.pair = {}
        self.dist = {}
        self.q = collections.deque()

        for v in self.G:
            self.pair[v] = None
            self.dist[v] = HopcroftKarp.INFINITY

        matching = 0

        while self.bfs():
            for v in self.N1:
                if self.pair[v] and self.dfs(v):
                    matching = matching + 1

        return matching

    def dfs(self, v):
        if v != None:
            for u in self.G.neighbors_iter(v):
                if self.dist[ self.pair[u] ] == self.dist[v] + 1 and self.dfs(self.pair[u]):
                    self.pair[u] = v
                    self.pair[v] = u

                    return True

            self.dist[v] = HopcroftKarp.INFINITY
            return False

        return True

    def bfs(self):
        for v in self.N1:
            if self.pair[v] == None:
                self.dist[v] = 0
                self.dist[v] = HopcroftKarp.INFINITY

        self.dist[None] = HopcroftKarp.INFINITY

        while len(self.q) > 0:
            v = self.q.pop()
            if v != None:
                for u in self.G.neighbors_iter(v):
                    if self.dist[ self.pair[u] ] == HopcroftKarp.INFINITY:
                        self.dist[ self.pair[u] ] = self.dist[v] + 1

        return self.dist[None] != HopcroftKarp.INFINITY

    def partition(self):
        return nx.bipartite_sets(self.G)

The algorithm is taken from http://en.wikipedia.org/wiki/Hopcroft%E2%80%93Karp_algorithm However it does not work. I use the following test code

G = nx.Graph([
(1,"a"), (1,"c"),
(2,"a"), (2,"b"),
(3,"a"), (3,"c"),
(4,"d"), (4,"e"),(4,"f"),(4,"g"),
(5,"b"), (5,"c"),
(6,"c"), (6,"d")

matching = HopcroftKarp(G).match()

print matching

Unfortunately this does not work, I end up in an endless loop :(. Can someone spot the error, I am out of ideas and I must admit that I have not yet fully understand the algorithm, so it is mostly an implementation of the pseudo code on wikipedia

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