We prove that for any fixed r ≥ 2, the tree-width of graphs not containing Kr as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph classes such as Kr-minor free graphs and graphs of bounded genus.

We introduce a new width parameter for matroids called decomposition width and prove that every matroid property expressible in the monadic second order logic can be computed in linear time for matroids with bounded decomposition width if their decomposition is given. Since decompositions of small width for our new notion can be computed in polynomial time for matroids of bounded branch-width r...

Disjunctive Answer Set Programming (ASP) is a powerful declarative programming paradigm whose main decision problems are located on the second level of the polynomial hierarchy. Identifying tractable fragments and developing efficient algorithms for such fragments are thus important objectives in order to complement the sophisticated ASP systems available to date. Hard problems can become tract...

Tree-width and clique-width are two important graph complexity measures that serve as parameters in many fixed-parameter tractable (FPT) algorithms. The same classes of sparse graphs, in particular of planar graphs and of graphs of bounded degree have bounded tree-width and bounded clique-width. We prove that, for sparse graphs, clique-width is polynomially bounded in terms of tree-width. For p...

We show that there exists a linear time algorithm for deciding whether a graph of bounded tree-width has clique-width k for some fixed integer k. Communicated by Giuseppe Liotta and Ioannis G. Tollis: submitted October 2001; revised July 2002 and February 2003. The work of the second author was supported by the German Research Association (DFG) grant WA 674/9-2. W. Espelage et al., Deciding Cli...

PETR HLINĚNÝ1,2,*, SANG-IL OUM3,7, DETLEF SEESE4 AND GEORG GOTTLOB5,6 Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic VŠB, Technical University of Ostrava, Ostrava, Czech Republic School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA Institute AIFB, University Karlsruhe (TH), D-76128 Karlsruhe, Germany Oxford University Comput...

1 T first question to ask in determining implant size is, who makes the choice? It would seem obvious that the patient decides. However, some plastic surgeons believe it is their responsibility to educate their patients about the alleged dangers of large implants and talk them down,1 a practice I have called paternalistic.2 Mallucci and Branford1 warn of serious consequences of large breast siz...

TomoEDGE is an advanced delivery form of tomotherapy which uses a dynamic secondary collimator. This plan comparison study describes the new features, their clinical applicability, and their effect on plan quality and treatment speed. For the first 45 patients worldwide that were scheduled for a treatment with TomoEdge, at least two plans were created: one with the previous "standard"mode with ...