A single-exponential FPT algorithm for the K4-minor cover problem

Given a graph G and a parameter k∈N, the parameterized K4-minor cover problem asks whether at most k vertices can be deleted to turn G into a K4-minor-free graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two well-studied parameterized vertex deletion problems, V...

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Vydáno v:Journal of computer and system sciences Ročník 81; číslo 1; s. 186 - 207
Hlavní autoři: Kim, Eun Jung, Paul, Christophe, Philip, Geevarghese
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.02.2015
Elsevier
Témata:
[formula omitted]-minor cover
Computer Science
Discrete Mathematics
Fixed-parameter tractable algorithms
Treewidth-2 Deletion
Treewidth-2 Deletion
Fixed-parameter tractable algorithms
K4-minor cover
FPT time
Vertex Cover
ISSN:0022-0000, 1090-2724
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Abstract Given a graph G and a parameter k∈N, the parameterized K4-minor cover problem asks whether at most k vertices can be deleted to turn G into a K4-minor-free graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can also be expressed as Treewidth-tVertex Deletion problems: t=0 for Vertex Cover and t=1 for Feedback Vertex Set. While single-exponential FPT algorithms, i.e. running in 2O(k)⋅nO(1) time, are known for these two latter problems, it was open whether the K4-minor cover problem could be solved in single-exponential FPT time. This paper answers this question in the affirmative. Observe that it is known to be unlikely that Treewidth-tVertex Deletion can be solved in time 2o(k)⋅nO(1). •We provide an efficient FPT algorithm for the K4-minor cover problem.•It combines iterative compression with protrusion reduction and branching.•It extends previous algorithms for Vertex Cover and Feedback Vertex Set.
AbstractList Given an input graph G and an integer k, the parameterized K4 -minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K4 -minor-free graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set , which can also be expressed as Treewidth- t Vertex Deletion problems: t = 0 for Vertex Cover and t = 1 for Feedback Vertex Set . While a single-exponential FPT algorithm has been known for a long time for Vertex Cover , such an algorithm for Feedback Vertex Set was devised comparatively recently. While it is known to be unlikely that Treewidth- t Vertex Deletion can be solved in time co ( k ) nO (1) , it was open whether the K4 -minor cover could be solved in single-exponential FPT time, i.e. in ck nO (1) time.
Given a graph G and a parameter k∈N, the parameterized K4-minor cover problem asks whether at most k vertices can be deleted to turn G into a K4-minor-free graph, or equivalently in a graph of treewidth at most 2. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can also be expressed as Treewidth-tVertex Deletion problems: t=0 for Vertex Cover and t=1 for Feedback Vertex Set. While single-exponential FPT algorithms, i.e. running in 2O(k)⋅nO(1) time, are known for these two latter problems, it was open whether the K4-minor cover problem could be solved in single-exponential FPT time. This paper answers this question in the affirmative. Observe that it is known to be unlikely that Treewidth-tVertex Deletion can be solved in time 2o(k)⋅nO(1). •We provide an efficient FPT algorithm for the K4-minor cover problem.•It combines iterative compression with protrusion reduction and branching.•It extends previous algorithms for Vertex Cover and Feedback Vertex Set.
Author Paul, Christophe
Kim, Eun Jung
Philip, Geevarghese
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Issue 1
Keywords Treewidth-2 Deletion
Fixed-parameter tractable algorithms
K4-minor cover
FPT time
Vertex Cover
Language English
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References Kloks (br0250) 1994; vol. 842
Valdes, Tarjan, Lawler (br0320) 1982; 11
Fomin, Lokshtanov, Saurabh, Thilikos (br0170) 2010
Fomin, Lokshtanov, Misra, Saurabh (br0190) 2012
Lewis, Yannakakis (br0280) 1980; 20
Joret, Paul, Sau, Saurabh, Thomassé (br0240) 2011; vol. 6942
Courcelle (br0090) 1990; 85
Heggernes, van 't Hof, Lokshtanov, Paul (br0210) 2011; vol. 13
Kim, Langer, Paul, Reidl, Rossmanith, Sau, Sikdar (br0260) 2013
Bodlaender, Fomin, Lokshtanov, Penninkx, Saurabh, Thilikos (br0040) 2009
Cao, Chen, 0002 (br0060) 2010; vol. 6139
Fomin, Lokshtanov, Misra, Philip, Saurabh (br0180) 2011; vol. 9
Reed, Smith, Vetta (br0300) 2004; 32
Chen, Fomin, Liu, Lu, Villanger (br0080) 2008; 74
Roberston, Seymour (br0310) 2004; 92
Bodlaender, de Fluiter (br0030) 1996; vol. 1136
Downey, Fellows (br0140) 1999
Dehne, Fellows, Langston, Rosamond, Stevens (br0110) 2007; 41
Hopcroft, Tarjan (br0220) 1973; 16
Flum, Grohe (br0160) 2006
Bodlaender, Fomin, Lokshtanov, Penninkx, Saurabh, Thilikos (br0050) 2013
Diestel (br0130) 2010; vol. 173
Guo, Gramm, Hüffner, Niedermeier, Wernicke (br0200) 2006; 72
Demaine, Fomin, Hajiaghayi, Thilikos (br0120) 2005; 52
Chen, Chor, Fellows, Huang, Juedes, Kanj, Xia (br0070) 2005; 201
Jansen, Lokshtanov, Saurabh (br0230) 2014
Bodlaender (br0020) 1998; 209
Eppstein (br0150) 1992; 98
Bidyuk, Dechter (br0010) 2007; 28
Lokshtanov, Marx, Saurabh (br0270) 2011
Cygan, Nederlof, Pilipczuk, Pilipczuk, van Rooij, Wojtaszczyk (br0100) 2011
Niedermeier (br0290) 2006; vol. 31
References_xml – start-page: 629
  year: 2009
  end-page: 638
  ident: br0040
  article-title: (Meta) Kernelization
  publication-title: Annual IEEE Symposium on Foundations of Computer Science
– start-page: 613
  year: 2013
  end-page: 624
  ident: br0260
  article-title: Linear kernels and single-exponential algorithms via protrusion decompositions
  publication-title: International Colloquium on Automata, Languages, and Programming
– year: 2006
  ident: br0160
  article-title: Parameterized Complexity Theory
  publication-title: Texts Theor. Comp. Sci.
– volume: vol. 13
  start-page: 217
  year: 2011
  end-page: 228
  ident: br0210
  article-title: Obtaining a bipartite graph by contracting few edges
  publication-title: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
– volume: vol. 6942
  start-page: 394
  year: 2011
  end-page: 407
  ident: br0240
  article-title: Hitting and harvesting pumpkins
  publication-title: European Symposium on Algorithms
– volume: vol. 1136
  start-page: 277
  year: 1996
  end-page: 289
  ident: br0030
  article-title: Parallel algorithms for series parallel graphs
  publication-title: European Symposium on Algorithms
– volume: 201
  start-page: 216
  year: 2005
  end-page: 231
  ident: br0070
  article-title: Tight lower bounds for certain parameterized NP-hard problems
  publication-title: Inf. Comput.
– start-page: 760
  year: 2011
  end-page: 776
  ident: br0270
  article-title: Slightly superexponential parameterized problems
  publication-title: Annual ACM-SIAM Symposium on Discrete Algorithms
– volume: 28
  start-page: 1
  year: 2007
  end-page: 48
  ident: br0010
  article-title: Cutset sampling for bayesian networks
  publication-title: J. Artif. Intell. Res.
– volume: 209
  start-page: 1
  year: 1998
  end-page: 45
  ident: br0020
  article-title: A partial k-arboretum of graphs with bounded treewidth
  publication-title: Theor. Comput. Sci.
– volume: 41
  start-page: 479
  year: 2007
  end-page: 492
  ident: br0110
  article-title: An
  publication-title: Theory Comput. Syst.
– start-page: 470
  year: 2012
  end-page: 479
  ident: br0190
  article-title: Planar
  publication-title: 53rd Annual IEEE Symposium on Foundations of Computer Science
– volume: vol. 173
  year: 2010
  ident: br0130
  article-title: Graph Theory
  publication-title: Grad. Texts Math.
– volume: vol. 842
  year: 1994
  ident: br0250
  article-title: Treewidth–Computations and Approximations
  publication-title: Lect. Notes Comput. Sci.
– volume: vol. 9
  start-page: 189
  year: 2011
  end-page: 200
  ident: br0180
  article-title: Hitting forbidden minors: approximation and kernelization
  publication-title: International Symposium on Theoretical Aspects of Computer Science
– start-page: 503
  year: 2010
  end-page: 510
  ident: br0170
  article-title: Bidimensionality and kernels
  publication-title: Annual ACM–SIAM symposium on Discrete algorithms
– volume: 52
  start-page: 866
  year: 2005
  end-page: 893
  ident: br0120
  article-title: Subexponential parameterized algorithms on bounded-genus graphs and
  publication-title: J. ACM
– year: 2013
  ident: br0050
  article-title: (Meta) Kernelization
– volume: 74
  start-page: 1188
  year: 2008
  end-page: 1198
  ident: br0080
  article-title: Improved algorithms for feedback vertex set problems
  publication-title: J. Comput. Syst. Sci.
– volume: 72
  start-page: 1386
  year: 2006
  end-page: 1396
  ident: br0200
  article-title: Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
  publication-title: J. Comput. Syst. Sci.
– year: 1999
  ident: br0140
  article-title: Parameterized Complexity
– volume: 11
  start-page: 298
  year: 1982
  end-page: 313
  ident: br0320
  article-title: The recognition of series-parallel graphs
  publication-title: SIAM J. Comput.
– volume: 16
  start-page: 372
  year: 1973
  end-page: 378
  ident: br0220
  article-title: Efficient algorithms for graph manipulation (algorithm 447)
  publication-title: Commun. ACM
– volume: vol. 6139
  start-page: 93
  year: 2010
  end-page: 104
  ident: br0060
  article-title: On feedback vertex set new measure and new structures
  publication-title: Scandinavian Workshops on Algorithm Theory
– start-page: 150
  year: 2011
  end-page: 159
  ident: br0100
  article-title: Solving connectivity problems parameterized by treewidth in single exponential time
  publication-title: Annual IEEE Symposium on Foundations of Computer Science
– volume: vol. 31
  year: 2006
  ident: br0290
  article-title: Invitation to Fixed Parameter Algorithms
  publication-title: Oxford Lect. Ser. Math. Appl.
– volume: 85
  start-page: 12
  year: 1990
  end-page: 75
  ident: br0090
  article-title: The monadic second-order logic of graphs (I): recognizable sets of finite graphs
  publication-title: Inf. Comput.
– volume: 98
  start-page: 41
  year: 1992
  end-page: 55
  ident: br0150
  article-title: Parallel recognition of series-parallel graphs
  publication-title: Inf. Comput.
– volume: 20
  start-page: 219
  year: 1980
  end-page: 230
  ident: br0280
  article-title: The node-deletion problem for hereditary properties is NP-complete
  publication-title: J. Comput. Syst. Sci.
– volume: 92
  start-page: 325
  year: 2004
  end-page: 357
  ident: br0310
  article-title: Graph minors XX: Wagner's conjecture
  publication-title: J. Comb. Theory B
– start-page: 1802
  year: 2014
  end-page: 1811
  ident: br0230
  article-title: A near-optimal planarization algorithm
  publication-title: Annual ACM–SIAM Symposium on Discrete Algorithms
– volume: 32
  start-page: 299
  year: 2004
  end-page: 301
  ident: br0300
  article-title: Finding odd cycle transversals
  publication-title: Oper. Res. Lett.
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Snippet Given a graph G and a parameter k∈N, the parameterized K4-minor cover problem asks whether at most k vertices can be deleted to turn G into a K4-minor-free...
Given an input graph G and an integer k, the parameterized K4 -minor cover problem asks whether there is a set S of at most k vertices whose deletion results...
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SubjectTerms [formula omitted]-minor cover
Computer Science
Discrete Mathematics
Fixed-parameter tractable algorithms
Treewidth-2 Deletion
Title A single-exponential FPT algorithm for the K4-minor cover problem
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