图问题的完美紧致对称破缺

2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) Pub Date : 2016-09-01 DOI:10.1109/SYNASC.2016.034

Marijn J. H. Heule

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引用次数: 6

摘要

对称破缺是解决许多图问题的关键技术。然而，目前最先进的技术只是部分地打破了图的对称性，导致搜索算法不必要地探索搜索空间的许多同构部分。研究了图问题的完全对称破缺的性质。对于小尺寸的图(小到5阶)，有一个令人惊讶的结果，那就是完美的对称性破缺可以用一个紧凑的命题公式来实现，其中每个字最多出现两次。至少对于小图，完全对称破缺可以比现有的(部分)对称破缺方法表达得更紧凑。我们提出了几种计算和分析完美对称破缺公式的技术。

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The Quest for Perfect and Compact Symmetry Breaking for Graph Problems

Symmetry breaking is a crucial technique to solve many graph problems. However, current state-of-the-art techniques break graph symmetries only partially, causing search algorithms to unnecessarily explore many isomorphic parts of the search space. We study properties of perfect symmetry breaking for graph problems. One promising and surprising result on small-sized graphs—up to order five— is that perfect symmetry breaking can be achieved using a compact propositional formula in which each literal occurs at most twice. At least for small graphs, perfect symmetry breaking can be expressed more compactly than the existing (partial) symmetry-breaking methods. We present several techniques to compute and analyze perfect symmetry-breaking formulas.

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2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

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