SUBOPTIMAL GRAPH ISOMORPHISM USING BIPARTITE MATCHING

Abstract

Graphs provide us with a flexible and powerful way to represent objects in various areas of computer science. One of the main drawbacks is, however, that many standard algorithms on graphs have a high computational complexity. The present paper considers the problem of graph isomorphism, i.e. checking two graphs for identity. A novel approach for the efficient computation of graph isomorphism is presented. The proposed algorithm is based on bipartite graph matching by means of an assignment algorithm. The algorithmic framework is suboptimal in the sense of possibly rejecting pairs of graphs without making a decision. As an advantage, however, it offers polynomial runtime. In experiments on diverse graph data sets we demonstrate substantial speedups of our proposed method over several standard procedures for graph isomorphism. Furthermore, although the computational framework for isomorphism is suboptimal, we show that the proposed algorithm rejects only very few pairs of graphs and otherwise returns correct results.