All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Polynomial Kernels

Gregory Gutin; Leo van Iersel; Matthias Mnich; Anders Yeo

doi:10.1007/978-3-642-15775-2_28

All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Polynomial Kernels

Gregory Gutin, Leo van Iersel, Matthias Mnich, Anders Yeo

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

A ternary permutation-csp is specified by a subset p of the symmetric group \mathcal s_3\mathcal s_3. An instance of such a problem consists of a set of variables v and a multiset of constraints, which are ordered triples of distinct variables of v. The objective is to find a linear ordering a of v that maximizes the number of triples whose rearrangement (under a) follows a permutation in p. We prove that all ternary permutation-csps parameterized above average have kernels with quadratic numbers of variables.

Original language	English
Title of host publication	Algorithms - ESA 2010
Subtitle of host publication	18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I
Publisher	Springer
Pages	326-337
DOIs	https://doi.org/10.1007/978-3-642-15775-2_28
Publication status	Published - 2010
Externally published	Yes

Publication series

Series	Lecture Notes in Computer Science
Volume	6346

Access to Document

10.1007/978-3-642-15775-2_28

Cite this

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title = "All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Polynomial Kernels",

abstract = "A ternary permutation-csp is specified by a subset p of the symmetric group \mathcal s_3\mathcal s_3. An instance of such a problem consists of a set of variables v and a multiset of constraints, which are ordered triples of distinct variables of v. The objective is to find a linear ordering a of v that maximizes the number of triples whose rearrangement (under a) follows a permutation in p. We prove that all ternary permutation-csps parameterized above average have kernels with quadratic numbers of variables.",

author = "Gregory Gutin and {van Iersel}, Leo and Matthias Mnich and Anders Yeo",

year = "2010",

doi = "10.1007/978-3-642-15775-2_28",

language = "English",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "326--337",

booktitle = "Algorithms - ESA 2010",

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Gutin, G, van Iersel, L, Mnich, M & Yeo, A 2010, All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Polynomial Kernels. in Algorithms - ESA 2010: 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I. Springer, Lecture Notes in Computer Science, vol. 6346, pp. 326-337. https://doi.org/10.1007/978-3-642-15775-2_28

All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Polynomial Kernels. / Gutin, Gregory; van Iersel, Leo; Mnich, Matthias et al.
Algorithms - ESA 2010: 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I. Springer, 2010. p. 326-337 (Lecture Notes in Computer Science, Vol. 6346).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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AB - A ternary permutation-csp is specified by a subset p of the symmetric group \mathcal s_3\mathcal s_3. An instance of such a problem consists of a set of variables v and a multiset of constraints, which are ordered triples of distinct variables of v. The objective is to find a linear ordering a of v that maximizes the number of triples whose rearrangement (under a) follows a permutation in p. We prove that all ternary permutation-csps parameterized above average have kernels with quadratic numbers of variables.

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Gutin G, van Iersel L, Mnich M, Yeo A. All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Polynomial Kernels. In Algorithms - ESA 2010: 18th Annual European Symposium, Liverpool, UK, September 6-8, 2010. Proceedings, Part I. Springer. 2010. p. 326-337. (Lecture Notes in Computer Science, Vol. 6346). doi: 10.1007/978-3-642-15775-2_28