All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Kernels with Quadratic Number of Vertices
G. Gutin, L. van Iersel, M. Mnich and A. Yeo
J. Comput. Syst. Sci. 2010.

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 rearrangement (under $\alpha$) follows a permutation in $\Pi$. We prove that every ternary Permutation-CSP parameterized above average has a kernel with a quadratic number of variables.

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