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arXiv · 1004.1956

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
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Abstract

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 ordering (under $α$) follows a permutation in $Π$. We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables.

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Gregory Gutin, Leo van Iersel, Matthias Mnich, Anders Yeo. 2011-07-08. All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Kernels with Quadratic Numbers of Variables. https://arxiv.org/abs/1004.1956

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