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

Abstract

A ternary Permutation-CSP is specified by a subset $\Pi$ 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 $\alpha$ of $V$ that maximizes the number of triples whose ordering (under $\alpha$) follows a permutation in $\Pi$. We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables.

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