Heuristic to reduce the complexity of complete bipartite graphs to accelerate the search for maximum weighted matchings with small error
<|reference_start|>Heuristic to reduce the complexity of complete bipartite graphs to accelerate the search for maximum weighted matchings with small error: 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].<|reference_end|>
@article{etzold2003heuristic,
    title={Heuristic to reduce the complexity of complete bipartite graphs to
  accelerate the search for maximum weighted matchings with small error},
    author={Daniel Etzold},
    journal={arXiv preprint arXiv:cs/0306123},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0306123},
    primaryClass={cs.DS}
}