Mathematics in Computer Science

, Volume 13, Issue 4, pp 533–548 | Cite as

Optimal Symmetry Breaking for Graph Problems

  • Marijn J. H. HeuleEmail author


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.


Graphs Symmetry breaking Satisfiability 

Mathematics Subject Classification

Primary 68R10 Secondary 90C35 



The author is supported by the National Science Foundation under Grant No. CCF-1526760 and acknowledges the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing grid resources that have contributed to the research results reported within this paper.


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Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of TexasAustinUSA

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