All ternary permutation constraint satisfaction problems parameterized above average have kernels with quadratic numbers of variables

Authors:
Gregory Gutin;Leo Van Iersel;Matthias Mnich;Anders Yeo
Affiliations:
Royal Holloway, University of London, United Kingdom;University of Canterbury, Christchurch, New Zealand;Technische Universiteit Eindhoven, Eindhoven, The Netherlands;Royal Holloway, University of London, United Kingdom
Venue:
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Year:
2010

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Abstract

A ternary Permutation-CSP is specified by a subset Π of the symmetric group S3. 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 α of V that maximizes the number of triples whose rearrangement (under α) follows a permutation in Π. We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables.