Parameterized Shifted Combinatorial Optimization

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Authors

GAJARSKÝ Jakub HLINĚNÝ Petr KOUTECKÝ Martin ONN Shmuel

Year of publication 2017
Type Article in Proceedings
Conference International Computing and Combinatorics Conference COCOON 2017 (LNCS, volume 10392)
MU Faculty or unit

Faculty of Informatics

Citation
Doi http://dx.doi.org/10.1007/978-3-319-62389-4_19
Field Informatics
Keywords Combinatorial optimization; Shifted problem; Treewidth; MSO logic; MSO partitioning
Description Shifted combinatorial optimization is a new nonlinear optimization framework which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. This framework captures well studied and diverse problems ranging from so-called vulnerability problems to sharing and partitioning problems. In particular, every standard combinatorial optimization problem has its shifted counterpart, which is typically much harder. Already with explicitly given input set the shifted problem may be NP-hard. In this article we initiate a study of the parameterized complexity of this framework. First we show that shifting over an explicitly given set with its cardinality as the parameter may be in XP, FPT or P, depending on the objective function. Second, we study the shifted problem over sets definable in MSO logic (which includes, e.g., the well known MSO partitioning problems). Our main results here are that shifted combinatorial optimization over MSO definable sets is in XP with respect to the MSO formula and the treewidth (or more generally clique-width) of the input graph, and is W[1]-hard even under further severe restrictions.
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