MuSha: Subgraph Matching by Multilevel Sharing

Abstract

Subgraph matching (SM) is a fundamental problem in graph data analysis. Real-world patterns used in graph analysis are often symmetric and contain isomorphic substructures, but existing SM algorithms fail to explore such properties. To fill this gap, we propose MuSha, a multi-objective optimization framework for SM, leveraging multilevel sharing of isomorphic substructure results to speed up SM and symmetry breaking to avoid directly computing symmetric results. To efficiently compute and cache intermediate results for sharing, MuSha applies worst-case optimal joins (WCOJs) and utilizes trie data structures to compress and index results. To enable multilevel sharing, MuSha solves a multi-objective optimization problem involving pattern decomposition, symmetry breaking, WCOJ orders, and trie structural orders. Experimental results demonstrate that MuSha outperforms the state of the art by up to two orders of magnitude on graphs of millions of vertices.