Experimental Evaluation of Counting Subgraph Isomorphisms in Classes of Bounded Expansion

Michael P. O'Brien, Blair D. Sullivan

Abstract: Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering and heavy-tailed degree distributions. As such, fixed-parameter tractable algorithms for bounded expansion classes may offer a promising framework for network analysis where other approaches have struggled to scale. However, there has been little work done in implementing and evaluating the performance of these structure-based algorithms. To this end we introduce CONCUSS, a proof-of-concept implementation of a generic algorithmic pipeline for classes of bounded expansion. In particular, we focus on using CONCUSS for subgraph isomorphism counting (also called motif or graphlet counting), which has been used extensively as a tool for analyzing biological and social networks. Through a broad set of experiments we first evaluate the interactions between implementation/engineering choices at multiple stages of the pipeline and their effects on overall run time. From there, we establish viability of the bounded expansion framework by demonstrating that in some scenarios CONCUSS achieves run times competitive with a popular algorithm for subgraph isomorphism counting that does not exploit graph structure. Finally, we empirically identify two particular ways in which future theoretical advances could alleviate bottlenecks in the algorithmic pipeline.