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

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 rank-decomposition of a graph (on contrary to the us...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 158; no. 7; pp. 851 - 867
Main Authors: Ganian, Robert, Hliněný, Petr
Format: Journal Article
Language:English
Published: Elsevier B.V 06.04.2010
Subjects:
Graph colouring
Myhill–Nerode theorem
Parameterized algorithm
Rank-width
Myhill–Nerode theorem
Graph colouring
Parameterized algorithm
Rank-width
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary: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 rank-decomposition 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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2009.10.018