Publication details

On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width

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Year of publication 2010
Type Article in Periodical
Magazine / Source Discrete Applied Mathematics
MU Faculty or unit

Faculty of Informatics

Field Informatics
Keywords rank-width; parameterized algorithms; graphs
Description Rank-width is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded clique-width. We propose a formal mathematical framework and tools for easy design of dynamic algorithms running directly on a rankdecomposition of a graph (on contrary to the usual approach which translates a rank decomposition into a clique-width expression, with a possible exponential jump in the parameter). The main advantage of this framework is a fine control over the runtime dependency on the rank-width parameter. Our new approach is linked to a work of Courcelle and Kanté [7] who first proposed algebraic expressions with a so-called bilinear graph product as a better way of handling rank-decompositions, and to a parallel recent research of Bui-Xuan, Telle and Vatshelle.
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