Experimental Evaluation of Counting Subgraph Isomorphisms in Classes of Bounded Expansion.

Counting subgraph isomorphisms (also called motifs or graphlets) has been used extensively as a tool for analyzing biological and social networks. Under standard complexity assumptions there is no polynomial time algorithm for this problem, which limits the applicability of these tools to large data sets. Recent techniques from parameterized complexity have led to an algorithmic framework for isomorphism counting whose worst case time complexity is linear in the number of vertices, provided that the input graph has certain structural characteristics, known as bounded expansion. Previous work has suggested that the restrictions of bounded expansion structure--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. However, there has been little work done in implementing and evaluating the performance of this algorithmic pipeline. To this end we introduced CONCUSS, an open-source software package for counting subgraph isomorphisms in classes of bounded expansion. Through a broad set of experiments we evaluate implementations of multiple stages of the pipeline and demonstrate that our structure-based algorithm can be up to an order of magnitude faster than a popular algorithm for isomorphism counting.