On parse trees and Myhill–Nerode-type tools for handling graphs of bounded rank-width
نویسندگان
چکیده
منابع مشابه
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 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 rankdecomposition into a clique-width expression, with a possible exponential ...
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We define rank-width of graphs to investigate clique-width. Rank-width is a complexity measure of decomposing a graph in a kind of tree-structure, called a rankdecomposition. We show that graphs have bounded rank-width if and only if they have bounded clique-width. It is unknown how to recognize graphs of clique-width at most k for fixed k > 3 in polynomial time. However, we find an algorithm r...
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This thesis studies a structural framework for representing graphs of bounded treewidth, called a [treewidth] t-parse. This is a natural extension of the Cattell–Dinneen [pathwidth] t-parses, which they used in their platform for finding forbidden minors. Our t-parses are quite useful for representing graphs (in parsed form) for the many dynamic programs that are available for graphs of bounded...
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Although there exist many polynomial algorithms for NP hard problems running on a bounded clique-width expression of the input graph, there exists only little comparable work on such algorithms for rank-width. We believe that one reason for this is the somewhat obscure and hard-to-grasp nature of rank-decompositions. Nevertheless, strong arguments for using the rank-width parameter have been gi...
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Rank-width is a rather new structural graph measure introduced by Oum and Seymour in 2003 in order to find an efficiently computable approximation of clique-width of a graph. Being a very nice graph measure indeed, the only serious drawback of rank-width was that it is virtually impossible to use a given rank-decomposition of a graph for running dynamic algorithms on it. We propose a new indepe...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2010
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.10.018