Every ternary permutation constraint satisfaction problem parameterized above average has a kernel with a quadratic number of variables

  • Authors:

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

  • Affiliations:

  • Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;University of Canterbury, Christchurch, New Zealand;Technische Universiteit Eindhoven, Eindhoven, The Netherlands;Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2012

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Abstract

A ternary Permutation-CSP is specified by a subset @P of the symmetric group 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 every ternary Permutation-CSP parameterized above average has a kernel with a quadratic number of variables.