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Finding heaviest H-subgraphs in real weighted graphs, with applications

Virginia Vassilevska·Ryan Williams·Raphael Yuster
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Abstract

For a graph G with real weights assigned to the vertices (edges), the MAX H-SUBGRAPH problem is to find an H-subgraph of G with maximum total weight, if one exists. The all-pairs MAX H-SUBGRAPH problem is to find for every pair of vertices u,v, a maximum H-subgraph containing both u and v, if one exists. Our main results are new strongly polynomial algorithms for the all-pairs MAX H-SUBGRAPH problem for vertex weighted graphs. We also give improved algorithms for the MAX-H SUBGRAPH problem for edge weighted graphs, and various related problems, including computing the first k most significant bits of the distance product of two matrices. Some of our algorithms are based, in part, on fast matrix multiplication.

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Virginia Vassilevska, Ryan Williams, Raphael Yuster. 2006-09-04. Finding heaviest H-subgraphs in real weighted graphs, with applications. https://arxiv.org/abs/cs/0609009

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