NDLI: Finding Branch-Decompositions and Rank-Decompositions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hlinn, Petr Oum, Sang-il
Copyright Year	2008
Abstract	We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most k if such exists. This algorithm works also for partitioned matroids. Both of these algorithms are fixed-parameter tractable, that is, they run in time $O(n^3)$ where n is the number of vertices / elements of the input, for each constant value of k and any fixed finite field. The previous best algorithm for construction of a branch-decomposition or a rank-decomposition of optimal width due to Oum and Seymour [J. Combin. Theory Ser. B, 97 (2007), pp. 385393] is not fixed-parameter tractable.
Starting Page	1012
Ending Page	1032
Page Count	21
File Format	PDF
ISSN	00975397
DOI	10.1137/070685920
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3
Volume Number	38
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-06-25
Access Restriction	Subscribed
Subject Keyword	branch-width rank-width clique-width fixed-parameter tractable algorithm Graph theory Graph algorithms matroid graph
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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Finding Branch-Decompositions and Rank-Decompositions