Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms 2010
DOI: 10.1137/1.9781611973075.42
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Algorithmic Lower Bounds for Problems Parameterized by Clique-width

Abstract: Many NP-hard problems can be solved efficiently when the input is restricted to graphs of bounded tree-width or clique-width. In particular, by the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the tree-width of the input graph. On the other hand if we restrict ourselves to graphs of clique-width at most t, then there are many natural problems for which the running time of the best known algorithms is of the f… Show more

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Cited by 37 publications
(40 citation statements)
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“…While ETH is now a widely believed assumption, and has been used as a starting point to prove running time lower bounds for numerous problems [5,4,11,18,17], SETH remains largely untouched (with one exception [21]). The reason for this is two-fold.…”
Section: Complexity Assumptionmentioning
confidence: 99%
“…While ETH is now a widely believed assumption, and has been used as a starting point to prove running time lower bounds for numerous problems [5,4,11,18,17], SETH remains largely untouched (with one exception [21]). The reason for this is two-fold.…”
Section: Complexity Assumptionmentioning
confidence: 99%
“…It is also somewhat surprising that this good news does not extend to List Coloring, Precoloring Extension or Equitable Coloring, all of which turn out to be hard for W [1]. Results of the preliminary version of this paper [13] have led to thorough investigations of structural parameterizations like treewidth or clique-width [9,16,17,27].…”
Section: Conclusion and Open Problemsmentioning
confidence: 99%
“…One should examine it separately for each problem whether the lower bound obtained this way is tight or not. Many of the more involved reductions from Clique use edge selection gadgets (see e.g., [48,51,79]). As a clique of size k has Θ(k 2 ) edges, this means that the reduction typically increases the parameter to Θ(k 2 ) at least and, similarly to Theorem 2.8, what we can conclude is that there is no f (k)n o( √ k) time algorithm for the target problem (unless ETH fails).…”
Section: Conjecture 25 (Strong Exponential Time Hypothesis [63 18])mentioning
confidence: 99%