All Ternary Permutation Constraint Satisfaction Problems Parameterized above Average Have Kernels with Quadratic Numbers of Variables

  • Gregory Gutin
  • Leo van Iersel
  • Matthias Mnich
  • Anders Yeo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6346)


A ternary Permutation-CSP is specified by a subset Π of the symmetric group \(\mathcal S_3\). 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 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.


Symmetric Group Logarithmic Sobolev Inequality Quadratic Number Binary Random Variable Tight Lower Bound 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gregory Gutin
    • 1
  • Leo van Iersel
    • 2
  • Matthias Mnich
    • 3
  • Anders Yeo
    • 1
  1. 1.Royal HollowayUniversity of LondonUnited Kingdom
  2. 2.University of CanterburyChristchurchNew Zealand
  3. 3.Technische Universiteit EindhovenEindhovenThe Netherlands

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