Accelerating Maximum Common Subgraph Computation by Exploiting Symmetries

2026-03-24

AI Summary

This work addresses the computational inefficiency of maximum common subgraph (MCS) solvers, which stems from the vast search space and inadequate handling of graph symmetries. We propose the first dual symmetry-breaking framework that simultaneously identifies modular symmetries in both the variable graph and the value graph based on local neighborhood structures. By leveraging equivalence class reasoning, our approach prunes isomorphic subtrees while preserving solution optimality. This method represents the first systematic integration of symmetry handling across both graphs, substantially enhancing pruning efficiency. Experimental results on standard MCS benchmarks demonstrate that our approach outperforms the current state-of-the-art RRSplit algorithm, solving more instances and significantly reducing both computation time and search space.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The Maximum Common Subgraph (MCS) problem plays a key role in many applications, including cheminformatics, bioinformatics, and pattern recognition, where it is used to identify the largest shared substructure between two graphs. Although symmetry exploitation is a powerful means of reducing search space in combinatorial optimization, its potential in MCS algorithms has remained largely underexplored due to the challenges of detecting and integrating symmetries effectively. Existing approaches, such as RRSplit, partially address symmetry through vertex-equivalence reasoning on the variable graph, but symmetries in the value graph remain unexploited. In this work, we introduce a complete dual-symmetry breaking framework that simultaneously handles symmetries in both variable and value graphs. Our method identifies and exploits modular symmetries based on local neighborhood structures, allowing the algorithm to prune isomorphic subtrees during search while rigorously preserving optimality. Extensive experiments on standard MCS benchmarks show that our approach substantially outperforms the state-of-the-art RRSplit algorithm, solving more instances with significant reductions in both computation time and search space. These results highlight the practical effectiveness of comprehensive symmetry-aware pruning for accelerating exact MCS computation.

Problem

• Maximum Common Subgraph
• Symmetry Exploitation
• Combinatorial Optimization
• Graph Isomorphism
• Search Space Pruning

Innovation

• symmetry breaking
• maximum common subgraph
• dual symmetry
• modular symmetry
• search space pruning