research-article

Clique Cover and Graph Separation: New Incompressibility Results

Authors:

Stefan Kratsch,

Marcin Pilipczuk,

Michał Pilipczuk, and

Magnus WahlströmAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 6, Issue 2

Article No.: 6, Pages 1 - 19

https://doi.org/10.1145/2594439

Published: 01 May 2014 Publication History

Abstract

The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. In this article, we show that, unless the polynomial hierarchy collapses to its third level, the following parameterized problems do not admit a polynomial-time preprocessing algorithm that reduces the size of an instance to polynomial in the parameter:

---Edge Clique Cover, parameterized by the number of cliques, ---Directed Edge/Vertex Multiway Cut, parameterized by the size of the cutset, even in the case of two terminals, ---Edge/Vertex Multicut, parameterized by the size of the cutset, and ---k-Way Cut, parameterized by the size of the cutset.

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Luo W(2022)On some FPT problems without polynomial Turing compressionsTheoretical Computer Science10.1016/j.tcs.2021.12.017905:C(87-98)Online publication date: 22-Feb-2022
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Alman JMnich MWilliams V(2020)Dynamic Parameterized Problems and AlgorithmsACM Transactions on Algorithms10.1145/339503716:4(1-46)Online publication date: 6-Jul-2020
https://dl.acm.org/doi/10.1145/3395037
Kratsch SWahlströM M(2020)Representative Sets and Irrelevant VerticesJournal of the ACM10.1145/339088767:3(1-50)Online publication date: 2-Jun-2020
https://doi.org/10.1145/3390887
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Index Terms

Clique Cover and Graph Separation: New Incompressibility Results
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 6, Issue 2

May 2014

98 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/2631196

Editor:
Eric Allender
Rutgers University, USA

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Copyright © 2014 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 May 2014

Accepted: 01 March 2014

Revised: 01 February 2014

Received: 01 January 2013

Published in TOCT Volume 6, Issue 2

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Cited By

Luo W(2022)On some FPT problems without polynomial Turing compressionsTheoretical Computer Science10.1016/j.tcs.2021.12.017905:C(87-98)Online publication date: 22-Feb-2022
https://dl.acm.org/doi/10.1016/j.tcs.2021.12.017
Alman JMnich MWilliams V(2020)Dynamic Parameterized Problems and AlgorithmsACM Transactions on Algorithms10.1145/339503716:4(1-46)Online publication date: 6-Jul-2020
https://dl.acm.org/doi/10.1145/3395037
Kratsch SWahlströM M(2020)Representative Sets and Irrelevant VerticesJournal of the ACM10.1145/339088767:3(1-50)Online publication date: 2-Jun-2020
https://doi.org/10.1145/3390887
Sun YWu CZhang XZhang Z(2020)Computation and algorithm for the minimum k-edge-connectivity of graphsJournal of Combinatorial Optimization10.1007/s10878-020-00541-z44:3(1741-1752)Online publication date: 15-Feb-2020
https://doi.org/10.1007/s10878-020-00541-z
Fomin FLokshtanov DSaurabh SZehavi M(2019)Kernelization10.1017/9781107415157Online publication date: 3-Jan-2019
https://doi.org/10.1017/9781107415157
Pilipczuk MWahlström M(2018)Directed Multicut is W[1]-hard, Even for Four Terminal PairsACM Transactions on Computation Theory10.1145/320177510:3(1-18)Online publication date: 23-May-2018
https://dl.acm.org/doi/10.1145/3201775
Fluschnik THermelin DNichterlein ANiedermeier R(2018)Fractals for Kernelization Lower BoundsSIAM Journal on Discrete Mathematics10.1137/16M108874032:1(656-681)Online publication date: 20-Mar-2018
https://doi.org/10.1137/16M1088740
Friedrich THercher C(2018)On the kernel size of clique cover reductions for random intersection graphsJournal of Discrete Algorithms10.1016/j.jda.2015.05.01434:C(128-136)Online publication date: 19-Dec-2018
https://dl.acm.org/doi/10.1016/j.jda.2015.05.014
Le VPeng S(2018)On the complete width and edge clique cover problemsJournal of Combinatorial Optimization10.1007/s10878-016-0106-936:2(532-548)Online publication date: 19-Dec-2018
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Damaschke P(2017)Calculating approximation guarantees for partial set cover of pairsOptimization Letters10.1007/s11590-017-1108-y11:7(1293-1302)Online publication date: 12-Jan-2017
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