An Optimal XP Algorithm for Hamiltonian Cycle on Graphs of Bounded Clique-Width

Bergougnoux, Benjamin; Kanté, Mamadou Moustapha; Kwon, O-joung

doi:10.1007/978-3-319-62127-2_11

Cited by 4 publications

(1 citation statement)

References 10 publications

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“…The complexity of these problems parameterized by clique-width is well-known. Indeed, for each of these problems, we have an ad-hoc n O(k) time algorithm with k the clique-width of a given k-expression [4,12]. On the other hand, little is known concerning rank-width and Q-rank-width.…”

Section: Max Cutmentioning

confidence: 99%

More applications of the d-neighbor equivalence: acyclicity and connectivity constraints

Bergougnoux¹,

Kanté²

2018

Preprint

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In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. For all these problems, we obtain 1) and n O(k) time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of the parameters and match asymptotically also the running time of the best algorithms for basic NP-hard problems such as Vertex Cover and Dominating Set. Our framework is based on the d-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013]. The results we obtain highlight the importance and the generalizing power of this equivalence relation on width measures. We also prove that this equivalence relation could be useful for Max Cut: a W[1]-hard problem parameterized by clique-width. For this latter problem, we obtain n O(k) , n O(k) and n 2 O(k) time algorithms parameterized respectively by clique-width, Q-rank-width and rank-width.

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Section: Max Cutmentioning

confidence: 99%

More applications of the d-neighbor equivalence: acyclicity and connectivity constraints

Bergougnoux¹,

Kanté²

2018

Preprint

Self Cite

View full text Add to dashboard Cite

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Digraphs of Bounded Width

Kreutzer

Kwon

2018

Springer Monographs in Mathematics

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Cliquewidth III: The Odd Case of Graph Coloring Parameterized by Cliquewidth

Golovach

Lokshtanov

Saurabh

et al. 2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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Max-Cut (MC), Edge Dominating Set (EDS), Graph Coloring (GC) and Hamiltonian Path (HP) on graphs of bounded cliquewidth have received significant attention as they can be formulated in MSO 2 (and therefore have linear-time algorithms on bounded treewidth graphs by the celebrated Courcelle's theorem), but cannot be formulated in MSO 1 (which would have yielded linear-time algorithms on bounded cliquewidth graphs by a well-known theorem of Courcelle, Makowsky, and Rotics). Each of these problems can be solved in time g(k)n f (k) on graphs of cliquewidth k. . This shows that GC behaves qualitatively different from the other three problems. To the best of our knowledge, GC is the first natural problem known to require exponential dependence on the parameter in the exponent of n.

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An Optimal XP Algorithm for Hamiltonian Cycle on Graphs of Bounded Clique-Width

Cited by 4 publications

References 10 publications

More applications of the d-neighbor equivalence: acyclicity and connectivity constraints

More applications of the d-neighbor equivalence: acyclicity and connectivity constraints

Digraphs of Bounded Width

Cliquewidth III: The Odd Case of Graph Coloring Parameterized by Cliquewidth

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