Subgraph Counting: Color Coding beyond Trees

Abstract

The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting) have received significant attention. Color coding is a very general and powerful algorithmic technique for subgraph counting. Color coding has been shown to be effective in several applications, but scalable implementations are only known for the special case of tree queries (i.e. queries of treewidth one). In this paper we present the first efficient distributed implementation for color coding that goes beyond tree queries: ouralgorithm applies to any query graph of treewidth 2. Since tree queries can be solved in time linear in the size of the data graph, our contribution is the first step into the realm of color codingfor queries that require superlinear worst case running time. This superlinear complexity leads to significant load balancing problems on graphs with heavy tailed degree distributions. Our algorithm works around high degree nodes in the data graph, and achieves very good runtime and scalability on a diverse collection of data and query graph pairs. We also provide a theoretical analysis of our algorithmic techniques, exhibiting asymptotic improvements in runtime on random graphs with power law degree distributions, a popular model for real world graphs.