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.
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.