图搜索问题的紧凑部分对称性破缺
Compact Partial Symmetry Breaking for Graph Search Problems
- Ben-Gurion University of the Negev（内盖夫本-古里安大学）
- Czech Technical University（捷克理工大学）
- Monash University（莫纳什大学）
- OPTIMA ARC Industrial Training and Transformation Centre（OPTIMA ARC 工业培训与转型中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于图模式、强度驱动且冗余感知的方法，构建紧凑的部分对称性破缺约束，在保持小规模的同时显著提升图搜索性能。
AI中文摘要：
图搜索问题中的对称性破缺仍然具有挑战性：完整的对称性破缺约束通常规模呈指数级，而部分方法则以精度换取可扩展性。我们引入了一种基于强度驱动、冗余感知的方法论，用于基于图模式构建紧凑的部分对称性破缺约束。每个模式对应于一个关于等式文字的布尔子句，可以直接集成到CP或SAT模型中。我们的方法增量地选择强且非冗余的图模式，产生部分对称性破缺，这些破缺在保持紧凑规模的同时，实现了对非规范图的大量剪枝。这为推导轻量级部分对称性破缺约束提供了一个原则性框架，这些约束比所有已发表的现有最优替代方案显著更精确。我们使用冗余比率度量，在多达25个顶点的图实例上评估所提出的约束。所得的部分对称性破缺仅占完整对称性破缺约束规模的一小部分，同时与先前定义的部分对称性破缺方法相比，在多个图搜索基准上带来了显著的性能提升。
英文摘要：
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.
