Finding Branch-Decompositions and Rank-Decompositions

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...

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Veröffentlicht in:SIAM journal on computing Jg. 38; H. 3; S. 1012 - 1032
Hauptverfasser: Hliněný, Petr, Oum, Sang-il
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Schlagworte:
Algorithms
Decomposition
Graphs
ISSN:0097-5397, 1095-7111
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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. 385-393] is not fixed-parameter tractable.
AbstractList 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. 385-393] is not fixed-parameter tractable.
Author Oum, Sang-il
Hliněný, Petr
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Snippet 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...
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Title Finding Branch-Decompositions and Rank-Decompositions
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