All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Kernels with Quadratic Number of Vertices ## AbstractA 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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