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

Daniel Etzold
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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].

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Daniel Etzold. 2003-06-23. Heuristic to reduce the complexity of complete bipartite graphs to accelerate the search for maximum weighted matchings with small error. https://arxiv.org/abs/cs/0306123

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