Finding heaviest H-subgraphs in real weighted graphs, with applications
<|reference_start|>Finding heaviest H-subgraphs in real weighted graphs, with applications: 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.<|reference_end|>
@article{vassilevska2006finding,
    title={Finding heaviest H-subgraphs in real weighted graphs, with applications},
    author={Virginia Vassilevska, Ryan Williams and Raphael Yuster},
    journal={arXiv preprint arXiv:cs/0609009},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0609009},
    primaryClass={cs.DS cs.DM}
}