Heuristic to reduce the complexity of complete bipartite graphs to accelerate the search for maximum weighted matchings with small error

Abstract

A maximum weighted matching for bipartite graphs $G=(A\cup B,E)$ can be found by using the algorithm of Edmonds and Karp with a Fibonacci Heap and a modified Dijkstra in $O(nm+n^2\log n)$ time where n is the number of nodes and m the number of edges. For the case that $|A|=|B|$ the number of edges is $n^2$ and therefore the complexity is $O(n^3)$. In this paper we want to present a simple heuristic method to reduce the number of edges of complete bipartite graphs $G=(A\cup B,E)$ with $|A|=|B|$ such that $m=n\log n$ and therefore the complexity of such that $m=n\log n$ and therefore the complexity of $O(n^2\log n)$. The weights of all edges in G must be uniformly distributed in [0,1].

5 pages, 2 figures