CompDP: A Framework for Concurrent Subgraph Counting under Connectivity Constraints

Abstract

The subgraph counting problem computes the number of subgraphs of a given graph that satisfy some constraints. Among various constraints imposed on a graph, those regarding the connectivity of vertices have great importance since they are indispensable for determining various graph substructures, e.g., paths and Steiner trees. The subgraph counting problem under connectivity constraints is also important because counting such substructures often corresponds to measuring the importance of a vertex in network infrastructures. Here, we must solve the subgraph counting problems multiple times to compute such an importance measure for every vertex. However, even solving a single subgraph counting is a computationally hard task, preventing us from solving it multiple times in a reasonable time. In this paper, we propose a dynamic programming framework that simultaneously counts subgraphs for every vertex by focusing on similar connectivity constraints. Experimental results show that the proposed method solved multiple subgraph counting problems about 10--20 times faster than the existing approach for many problem settings.