Breaking symmetries with lex implications

Michael Codish, Thorsten Ehlers, Graeme Gange, Avraham Itzhakov, Peter J. Stuckey

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Breaking symmetries is crucial when solving hard combinatorial problems. A common way to eliminate symmetries in CP/SAT is to add symmetry breaking constraints. Ideally, symmetry breaking constraints should be complete and compact. The aim of this paper is to find compact and complete symmetry breaks applicable when solving hard combinatorial problems using CP/SAT approach. In particular: graph search problems and matrix model problems where symmetry breaks are often specified in terms of lex constraints. We show that sets of lex constraints can be expressed with only a small portion of their inner lex implications which are a particular form of Horn clauses. We exploit this fact and compute a compact encoding of the row-wise LexLeader and state of the art partial symmetry breaking constraints. We illustrate the approach for graph search problems and matrix model problems.

Original languageEnglish
Title of host publicationFunctional and Logic Programming - 14th International Symposium, FLOPS 2018, Proceedings
EditorsJohn P. Gallagher, Martin Sulzmann, John P. Gallagher
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783319906850
StatePublished - 1 Jan 2018
Event14th International Symposium on Functional and Logic Programming, FLOPS 2018 - Nagoya, Japan
Duration: 9 May 201811 May 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10818 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Symposium on Functional and Logic Programming, FLOPS 2018

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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