Discovering Locally Maximal Bipartite Subgraphs

TL;DR

This paper introduces three heuristic algorithms—greedy, simulated annealing, and genetic—for efficiently discovering locally maximal bipartite subgraphs in large graphs, comparing their performance to exact solutions obtained via SAT-solvers.

Contribution

It proposes and evaluates three novel heuristics for finding locally maximal bipartite subgraphs, addressing computational challenges of the global maximality problem.

Findings

Heuristics are faster than exact methods on large graphs.

Heuristics find large bipartite subgraphs with high vertex counts.

Trade-offs observed between solution quality and computational time.

Abstract

Induced bipartite subgraphs of maximal vertex cardinality are an essential concept for the analysis of graphs. Yet, discovering them in large graphs is known to be computationally hard. Therefore, we consider in this work a weaker notion of this problem, where we discard the maximality constraint in favor of inclusion maximality. Thus, we aim to discover locally maximal bipartite subgraphs. For this, we present three heuristic approaches to extract such subgraphs and compare their results to the solutions of the global problem. For the latter, we employ the algorithmic strength of fast SAT-solvers. Our three proposed heuristics are based on a greedy strategy, a simulated annealing approach, and a genetic algorithm, respectively. We evaluate all four algorithms with respect to their time requirement and the vertex cardinality of the discovered bipartite subgraphs on several benchmark datasets