An O(c^k n) 5-Approximation Algorithm for Treewidth

We give an algorithm that for an input n-vertex graph G and integer k > 0, in time O(c k n) either outputs that the tree width of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for tree width wh...

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Bibliographic Details
Published inAnnual Symposium on Foundations of Computer Science pp. 499 - 508
Main Authors Bodlaender, Hans L., Drange, Pal Gronas, Dregi, Markus S., Fomin, Fedor V., Lokshtanov, Daniel, Pilipczuk, Michal
Format Conference Proceeding
LanguageEnglish
Japanese
Published IEEE 01.10.2013
Subjects
approximation
Approximation algorithms
Approximation methods
Dynamic programming
fixed-parameter tractability
Heuristic algorithms
Particle separators
Partitioning algorithms
Polynomials
treewidth
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ISSN0272-5428
DOI10.1109/FOCS.2013.60

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Summary:We give an algorithm that for an input n-vertex graph G and integer k > 0, in time O(c k n) either outputs that the tree width of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for tree width which runs in time single-exponential in k and linear in n. Tree width based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single-exponential in the tree width and linear in the input size.
ISSN:0272-5428
DOI:10.1109/FOCS.2013.60