Compact Partial Symmetry Breaking for Graph Search Problems

Abstract

Symmetry breaking in graph search problems remains challenging: complete symmetry breaking constraints are typically exponential in size, while partial approaches trade precision for scalability. We introduce a strength-driven, redundancy-aware methodology for constructing compact partial symmetry breaking constraints based on graph patterns. Each pattern corresponds to a Boolean clause over equality literals and can be integrated directly into CP or SAT models. Our approach incrementally selects strong, non-redundant graph patterns, yielding partial symmetry breaks that achieve substantial pruning of non-canonical graphs while remaining compact in size. This provides a principled framework for deriving lightweight partial symmetry breaking constraints which are significantly more precise than all published state-of-the-art alternatives. We evaluate the proposed constraints on graph instances with up to 25 vertices using a redundancy ratio metric. The resulting partial symmetry breaks constitute only a small fraction of the size of complete symmetry breaking constraints, while delivering significant performance improvements across several graph search benchmarks compared to previously defined partial symmetry breaking methods.