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

TL;DR

This paper introduces new strongly polynomial algorithms for finding maximum H-subgraphs in weighted graphs, improving efficiency for vertex and edge weighted cases and related matrix computations.

Contribution

It presents novel algorithms for the all-pairs MAX H-SUBGRAPH problem in vertex weighted graphs and improves existing algorithms for edge weighted graphs and related problems.

Findings

Developed strongly polynomial algorithms for vertex weighted graphs.

Enhanced algorithms for edge weighted graphs and distance matrix computations.

Some algorithms utilize fast matrix multiplication techniques.

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.