Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking

Michael Codish; Michael Frank; Avraham Itzhakov; Alice Miller

doi:10.1007/s10601-016-9240-3

Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking

Michael Codish, Michael Frank, Avraham Itzhakov, Alice Miller

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value R(4, 3, 3) = 30. Along the way it is required to first compute the previously unknown set ℛ(3 , 3 , 3 ; 13) consisting of 78,892 Ramsey colorings.

Original language	English
Pages (from-to)	375-393
Number of pages	19
Journal	Constraints
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/s10601-016-9240-3
State	Published - 1 Jul 2016

Keywords

Ramsey numbers
SAT solving
Symmetry breaking

ASJC Scopus subject areas

Software
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Artificial Intelligence

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10.1007/s10601-016-9240-3

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title = "Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking",

abstract = "The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value R(4, 3, 3) = 30. Along the way it is required to first compute the previously unknown set ℛ(3 , 3 , 3 ; 13) consisting of 78,892 Ramsey colorings.",

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AU - Frank, Michael

AU - Itzhakov, Avraham

AU - Miller, Alice

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AB - The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value R(4, 3, 3) = 30. Along the way it is required to first compute the previously unknown set ℛ(3 , 3 , 3 ; 13) consisting of 78,892 Ramsey colorings.

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KW - Symmetry breaking

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Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking

Abstract

Keywords

ASJC Scopus subject areas

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