Article
On the PathWidth of Planar Graphs.
SIAM J. Discrete Math 01/2009; 23:13111316. DOI: 10.1137/060670146
Source: DBLP

Article: Méthodes Algorithmiques, Simulation et Combinatoire pour l'OpTimisation des TElécommunications

Conference Paper: Nondeterministic Graph Searching: From Pathwidth to Treewidth.
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ABSTRACT: We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this gametheoretic approach and graph decompositions called q branched tree decompositions, which can be interpreted as a parameterized version of tree decompositions. Path decomposition and (standard) tree decomposition are two extreme cases of qbranched tree decompositions. The equivalence between nondeterministic graph searching and qbranched tree decomposition enables us to design an exact (exponential time) algorithm computing qbranched treewidth for all q≥0, which is thus valid for both treewidth and pathwidth. This algorithm performs as fast as the best known exact algorithm for pathwidth. Conversely, this equivalence also enables us to design a lower bound on the amount of nondeterminism required to search a graph with the minimum number of searchers.Mathematical Foundations of Computer Science 2005, 30th International Symposium, MFCS 2005, Gdansk, Poland, August 29  September 2, 2005, Proceedings; 01/2005  [Show abstract] [Hide abstract]
ABSTRACT: A graph parameter is selfdual in some class of graphs embeddable in some surface if its value does not change in the dual graph more than a constant factor. Selfduality has been examined for several widthparameters, such as branchwidth, pathwidth, and treewidth. In this paper, we give a direct proof of the selfduality of branchwidth in graphs embedded in some surface. In this direction, we prove that bw(G ) 6 bw(G) + 2g 4 for any graph G embedded in a surface of Euler genus g.Discrete Applied Mathematics 10/2011; 159:21842186. · 0.72 Impact Factor
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