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

TL;DR

This paper introduces RRSplit, a backtracking algorithm for maximum common subgraph search that combines practical efficiency with theoretical guarantees, outperforming existing methods significantly.

Contribution

RRSplit is a novel algorithm that reduces redundancy in backtracking for maximum common subgraph search, achieving both efficiency and worst-case complexity guarantees.

Findings

RRSplit outperforms state-of-the-art algorithms by several orders of magnitude.

Theoretical analysis confirms RRSplit's worst-case time complexity matches the best known bounds.

Extensive experiments validate the practical efficiency of RRSplit on benchmark datasets.

Abstract

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 four benchmark graph collections, and the results demonstrate that our algorithm outperforms the practical state-of-the-art by several orders of magnitude.