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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| Vydané v: | Discrete Applied Mathematics Ročník 158; číslo 7; s. 851 - 867 |
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Elsevier B.V
06.04.2010
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Ganian, Robert Hliněný, Petr |
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| Cites_doi | 10.1016/S0166-218X(99)00184-5 10.1016/j.jctb.2005.10.006 10.1007/s002249910009 10.1016/0095-8956(86)90043-2 10.1016/j.dam.2008.08.026 10.1016/S0304-3975(02)00725-9 10.1016/0095-8956(91)90061-N 10.1016/j.dam.2009.09.009 10.1016/j.jctb.2005.08.005 10.1016/j.tcs.2007.03.043 10.1137/S0097539701385351 10.1016/j.jctb.2005.03.003 10.1016/S0166-218X(02)00198-1 10.1016/j.apal.2004.01.007 10.1016/0890-5401(90)90043-H 10.1137/070685920 10.1007/978-3-642-10217-2_27 |
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| Keywords | Myhill–Nerode theorem Graph colouring Parameterized algorithm Rank-width |
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