Fast Maximum Common Subgraph Search: A Redundancy-Reduced Backtracking Approach

Given two input graphs, finding the largest subgraph that occurs in both, i.e., finding the maximum common subgraph, is a fundamental operator for evaluating the similarity between two graphs in graph data analysis. Existing works for solving the problem are of either theoretical or practical interest, but not both. Specifically, the algorithms with a theoretical guarantee on the running time are known to be not practically efficient; algorithms following the recently proposed backtracking framework called McSplit, run fast in practice but do not have any theoretical guarantees. In this paper, we propose a new backtracking algorithm called RRSplit, which at once achieves better practical efficiency and provides a non-trivial theoretical guarantee on the worst-case running time. To achieve the former, we develop a series of reductions and upper bounds for reducing redundant computations, i.e., the time for exploring some unpromising branches of exploration that hold no maximum common subgraph. To achieve the latter, we formally prove that RRSplit incurs a worst-case time complexity which matches the best-known complexity for the problem. Finally, we conduct extensive experiments on several benchmark graph collections, and the results demonstrate that our algorithm outperforms the practical state-of-the-art by several orders of magnitude.