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Parameterized Shifted Combinatorial Optimization

  • Jakub Gajarský
  • Petr Hliněný
  • Martin Koutecký
  • Shmuel Onn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10392)

Abstract

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.

Keywords

Combinatorial optimization Shifted problem Treewidth MSO logic MSO partitioning 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jakub Gajarský
    • 1
    • 4
  • Petr Hliněný
    • 1
  • Martin Koutecký
    • 2
  • Shmuel Onn
    • 3
  1. 1.Masaryk UniversityBrnoCzech Republic
  2. 2.Charles UniversityPragueCzech Republic
  3. 3.Technion - Israel Institute of TechnologyHaifaIsrael
  4. 4.Technical University BerlinBerlinGermany

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