Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms 2009
DOI: 10.1137/1.9781611973068.90
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Clique-width: On the Price of Generality

Abstract: Many hard problems can be solved efficiently when the input is restricted to graphs of bounded treewidth. By the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the treewidth of the input graph. Moreover, for every fixed k ≥ 0, such problems can be solved in linear time on graphs of treewidth at most k. In particular, this implies that basic problems like Dominating Set, Graph Coloring, Clique, and Hamiltonian C… Show more

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Cited by 32 publications
(31 citation statements)
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References 19 publications
(34 reference statements)
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“…Even though our results in [13] resolve the parameterized complexity of these problems, the conclusion that unless FPT = W [1], there is no algorithm with run time O(g(t) · n c ), for some function g and a constant c not depending on t, is weak to compare the known algorithmic upper bounds. In this paper, we provide asymptotically tight optimal lower bounds for MAX-CUT and EDGE DOMINATING SET.…”
Section: Introductionmentioning
confidence: 74%
See 1 more Smart Citation
“…Even though our results in [13] resolve the parameterized complexity of these problems, the conclusion that unless FPT = W [1], there is no algorithm with run time O(g(t) · n c ), for some function g and a constant c not depending on t, is weak to compare the known algorithmic upper bounds. In this paper, we provide asymptotically tight optimal lower bounds for MAX-CUT and EDGE DOMINATING SET.…”
Section: Introductionmentioning
confidence: 74%
“…Even the existence of fixed parameter tractable algorithms (with clique-width being the parameter) for all these problems (or their generalizations) was open until very recently [15,22,23,24,17]. As the first step toward obtaining lower bounds for clique-width parameterizations, we have shown in [13] that unless FPT = W [1], there is no algorithm with run time O(g(t) · n c ), for some function g and a constant c not depending on t, for GRAPH COLORING, EDGE DOMINATING SET and HAMILTONIAN PATH.…”
Section: Introductionmentioning
confidence: 99%
“…Hence, it is natural to research whether one can improve the FPT result for Coloring from treewidth to clique-width. However, Fomin et al [24] showed that Coloring is W[1]-hard when parameterized by the clique-width of the input graph. We also note that Precoloring Extension is NP-complete for distance-hereditary graphs [4], which have clique-width at most 3 [29].…”
Section: Parameterized Coloring Problemsmentioning
confidence: 99%
“…[5]. On the other hand, [9] recently proved that various problems, such as the chromatic number or hamiltonicity, can not be solved by FPT algorithms parameterized by clique-/ rank-width.…”
Section: Definitions and Basicsmentioning
confidence: 99%