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 rearrangement (under α) follows a permutation in Π. We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables.
Part of this research has been supported by the EPSRC, grant EP/E034985/1, the Netherlands Organisation for Scientific Research (NWO), grant 639.033.403, and the Allan Wilson Centre for Molecular Ecology and Evolution.
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Gutin, G., van Iersel, L., Mnich, M., Yeo, A. (2010). All Ternary Permutation Constraint Satisfaction Problems Parameterized above Average Have Kernels with Quadratic Numbers of Variables. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_28
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