article

Intractability of Clique-Width Parameterizations

Authors:

Fedor V. Fomin,

Petr A. Golovach,

Daniel Lokshtanov,

Saket SaurabhAuthors Info & Claims

SIAM Journal on Computing, Volume 39, Issue 5

Pages 1941 - 1956

Published: 01 February 2010 Publication History

Abstract

We show that Edge Dominating Set, Hamiltonian Cycle, and Graph Coloring are $W[1]$-hard parameterized by clique-width. It was an open problem, explicitly mentioned in several papers, whether any of these problems is fixed parameter tractable when parameterized by the clique-width, that is, solvable in time $g(k)\cdot n^{O(1)}$ on $n$-vertex graphs of clique-width $k$, where $g$ is some function of $k$ only. Our results imply that the running time $O(n^{f(k)})$ of many clique-width-based algorithms is essentially the best we can hope for (up to a widely believed assumption from parameterized complexity, namely $FPT\neq W[1]$).

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Cited By

Ducoffe G(2022)Optimal Centrality Computations Within Bounded Clique-Width GraphsAlgorithmica10.1007/s00453-022-01015-w84:11(3192-3222)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1007/s00453-022-01015-w
Coudert DDucoffe GPopa A(2019)Fully Polynomial FPT Algorithms for Some Classes of Bounded Clique-width GraphsACM Transactions on Algorithms10.1145/331022815:3(1-57)Online publication date: 7-Jun-2019
https://dl.acm.org/doi/10.1145/3310228
Fomin FGolovach PLokshtanov DSaurabh SZehavi M(2018)Clique-width IIIACM Transactions on Algorithms10.1145/328082415:1(1-27)Online publication date: 16-Nov-2018
https://dl.acm.org/doi/10.1145/3280824
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Intractability of Clique-Width Parameterizations
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory

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cover image SIAM Journal on Computing

SIAM Journal on Computing Volume 39, Issue 5

January 2010

446 pages

ISSN:0097-5397

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 February 2010

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Cited By

Ducoffe G(2022)Optimal Centrality Computations Within Bounded Clique-Width GraphsAlgorithmica10.1007/s00453-022-01015-w84:11(3192-3222)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1007/s00453-022-01015-w
Coudert DDucoffe GPopa A(2019)Fully Polynomial FPT Algorithms for Some Classes of Bounded Clique-width GraphsACM Transactions on Algorithms10.1145/331022815:3(1-57)Online publication date: 7-Jun-2019
https://dl.acm.org/doi/10.1145/3310228
Fomin FGolovach PLokshtanov DSaurabh SZehavi M(2018)Clique-width IIIACM Transactions on Algorithms10.1145/328082415:1(1-27)Online publication date: 16-Nov-2018
https://dl.acm.org/doi/10.1145/3280824
Curticapean RMarx D(2016)Tight conditional lower bounds for counting perfect matchings on graphs of bounded treewidth, cliquewidth, and genusProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884548(1650-1669)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884548
González-Ruiz JMarcial-Romero JHernández-Servín J(2016)Computing the Clique-width of Cactus GraphsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2016.11.005328:C(47-57)Online publication date: 8-Dec-2016
https://dl.acm.org/doi/10.1016/j.entcs.2016.11.005
Sæther STelle J(2016)Between Treewidth and Clique-WidthAlgorithmica10.1007/s00453-015-0033-775:1(218-253)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1007/s00453-015-0033-7
Kintali SKothari NKumar A(2015)Approximation algorithms for digraph width parametersTheoretical Computer Science10.1016/j.tcs.2014.10.009562:C(365-376)Online publication date: 11-Jan-2015
https://dl.acm.org/doi/10.1016/j.tcs.2014.10.009
Lampis M(2012)Algorithmic Meta-theorems for Restrictions of TreewidthAlgorithmica10.5555/3118216.311828364:1(19-37)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.5555/3118216.3118283
Downey R(2012)A basic parameterized complexity primerThe Multivariate Algorithmic Revolution and Beyond10.5555/2344236.2344247(91-128)Online publication date: 1-Jan-2012
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Doucha MKratochvíl J(2012)Cluster vertex deletionProceedings of the 37th international conference on Mathematical Foundations of Computer Science10.1007/978-3-642-32589-2_32(348-359)Online publication date: 27-Aug-2012
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