A Parallel Algorithm for Subgraph Isomorphism

Abstract

In different application fields, such as biology, databases, social networks and so on, graphs are a widely adopted structure to represent the data. In these fields, a relevant problem is the detection and the localization of structural patterns within very large graphs; such a problem, formalized as subgraph isomorphism, has been proven to be NP-Complete in the general case. Moreover, the continuously growing size of the graphs to face, actually of hundred thousands of nodes, is making the problem even more challenging also for the most efficient algorithms in the state of the art, requiring days or weeks of computational time. This huge amount of time is also consequence of the fact that most of the algorithms do not exploit any kind of parallelism, even if the problem is suitable to be solved adopting parallel approaches. In this paper we present a new parallel algorithm for subgraph isomorphism, namely VF3P, based on a redesign of the well known algorithm VF3. The effectiveness of VF3P has been experimentally proven on a publicly available dataset of very large graphs, confirming that the algorithm is able to efficiently scale w.r.t. the number of used CPUs without affecting the memory usage.