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@inproceedings{1392992,
author = {Gajarský, Jakub and Hliněný, Petr and Koutecký, Martin and Onn, Shmuel},
address = {Hong Kong},
booktitle = {International Computing and Combinatorics Conference COCOON 2017 (LNCS, volume 10392)},
doi = {http://dx.doi.org/10.1007/978-3-319-62389-4_19},
editor = {Y. Cao and J. Chen},
keywords = {Combinatorial optimization; Shifted problem; Treewidth; MSO logic; MSO partitioning},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Hong Kong},
isbn = {978-3-319-62388-7},
pages = {224-236},
publisher = {Springer International Publishing AG},
title = {Parameterized Shifted Combinatorial Optimization},
year = {2017}
}
TY - JOUR
ID - 1392992
AU - Gajarský, Jakub - Hliněný, Petr - Koutecký, Martin - Onn, Shmuel
PY - 2017
TI - Parameterized Shifted Combinatorial Optimization
PB - Springer International Publishing AG
CY - Hong Kong
SN - 9783319623887
KW - Combinatorial optimization
KW - Shifted problem
KW - Treewidth
KW - MSO logic
KW - MSO partitioning
N2 - 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.
ER -
GAJARSKÝ, Jakub, Petr HLINĚNÝ, Martin KOUTECKÝ and Shmuel ONN. Parameterized Shifted Combinatorial Optimization. In Y. Cao and J. Chen. \textit{International Computing and Combinatorics Conference COCOON 2017 (LNCS, volume 10392)}. Hong Kong: Springer International Publishing AG, 2017, p.~224-236. ISBN~978-3-319-62388-7. Available from: https://dx.doi.org/10.1007/978-3-319-62389-4\_{}19.
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