Approximating Rank-Width and Clique-Width Quickly

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Rank-width was defined by Oum and Seymour [ 2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most f(k) for some function f or confirms that rank-width is larger than k in time O(vertical bar V vertical bar(9) log vertical bar V vertical bar) for an input graph G = (V, E) and a fixed k. We develop three separate algorithms of this kind with faster running time. We construct an O(vertical bar V vertical bar(4))-time algorithm with f(k) = 3k + 1 by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an O(vertical bar V vertical bar(3))-time algorithm with f(k) = 24k, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hlineny [2005]. Finally we construct an O(vertical bar V vertical bar(3))-time algorithm with f(k) = 3k - 1 by combining the ideas of the two previously cited papers.
Publisher
ASSOCIATION FOR COMPUTING MACHINARY, INC.
Issue Date
2008-11
Language
English
Article Type
Article
Keywords

VERTEX-MINORS; BRANCH-WIDTH; GRAPHS; OBSTRUCTIONS; ALGORITHMS

Citation

ACM TRANSACTIONS ON ALGORITHMS , v.5, no.1, pp.1 - 20

ISSN
1549-6325
DOI
10.1145/1435375.1435385
URI
http://hdl.handle.net/10203/9386
Appears in Collection
MA-Journal Papers(저널논문)
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