Computing branchwidth via efficient triangulations and blocks

Minimal triangulations and potential maximal cliques are the main ingredients for a number of polynomial time algorithms on different graph classes computing the treewidth of a graph. Potential maximal cliques are also the main engine of the fastest so far, exact (exponential) treewidth algorithm. B...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 157; no. 12; pp. 2726 - 2736
Main Authors: Fomin, Fedor V., Mazoit, Frédéric, Todinca, Ioan
Format: Journal Article Conference Proceeding
Language:English
Published: Kidlington Elsevier B.V 28.06.2009
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Branchwidth
Combinatorics
Combinatorics. Ordered structures
Computer Science
Computer science; control theory; systems
Discrete Mathematics
Exact sciences and technology
Exponential time algorithm
Graph
Information retrieval. Graph
Mathematics
Sciences and techniques of general use
Theoretical computing
Branchwidth
Graph
Exponential time algorithm
Triangulation
Computer theory
Potential
Computing
Combinatorics
Optimization
Graph algorithm
Polynomial time
exponential time algorithm
graph
branchwidth
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:Minimal triangulations and potential maximal cliques are the main ingredients for a number of polynomial time algorithms on different graph classes computing the treewidth of a graph. Potential maximal cliques are also the main engine of the fastest so far, exact (exponential) treewidth algorithm. Based on the recent results of Mazoit, we define the structures that can be regarded as minimal triangulations and potential maximal cliques for branchwidth: efficient triangulations and blocks. We show how blocks can be used to construct an algorithm computing the branchwidth of a graph on n vertices in time ( 2 3 ) n ⋅ n O ( 1 ) .
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2008.08.009