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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| Published in: | SIAM journal on computing Vol. 38; no. 3; pp. 1012 - 1032 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2008
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| Subjects: | |
| ISSN: | 0097-5397, 1095-7111 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0097-5397 1095-7111 |
| DOI: | 10.1137/070685920 |