INTRACTABILITY OF CLIQUE-WIDTH PARAMETERIZATIONS

• Published in: SIAM journal on computing Vol. 39; no. 5; pp. 1941 - 1956
• Main Authors: FOMIN, Fedor V, GOLOVACH, Petr A, LOKSHTANOV, Daniel, SAURABH, Saket
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 2010
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Combinatorics; Combinatorics. Ordered structures; Complexity theory; Computation; Computer science; control theory; systems; Exact sciences and technology; Graph coloring; Graph theory; Graphs; Mathematical analysis; Mathematical models; Mathematics; Miscellaneous; Parameter optimization; Parametrization; Running; Sciences and techniques of general use; Studies; Symbols; Theoretical computing; Clique width; 68Q25; 68W40; tree-width; Hamiltonian cycle; Dominating set; Graph clique; 68Q17; parameterized complexity; Vertex(graph); Parameterization; Algorithm; Chromatic number; Complexity; Hamiltonian graph; Tree width; clique-width; edge domination; Graph colouring; Edge set; Cycle(graph)
• ISSN: 0097-5397; 1095-7111
• DOI: 10.1137/080742270

The authors show that Edge Dominating Set, Hamiltonian Cycle, and Graph Coloring are ... 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 ... on n-vertex graphs of clique-width k, where g is some function of k only. The results imply that the running time ... of many clique-width-based algorithms is essentially the best they can hope for (up to a widely believed assumption from parameterized complexity, namely ... ).(ProQuest: ... denotes formulae/symbols omitted.)