Exact Algorithms for Treewidth and Minimum Fill-In

We show that the treewidth and the minimum fill-in of an $n$-vertex graph can be computed in time $\mathcal{O}(1.8899^n)$. Our results are based on combinatorial proofs that an $n$-vertex graph has $\mathcal{O}(1.7087^n)$ minimal separators and $\mathcal{O}(1.8135^n)$ potential maximal cliques. We a...

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Bibliographic Details
Published in:SIAM journal on computing Vol. 38; no. 3; pp. 1058 - 1079
Main Authors: Fomin, Fedor V., Kratsch, Dieter, Todinca, Ioan, Villanger, Yngve
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Subjects:
Algorithms
Approximation
Computer Science
Data Structures and Algorithms
Dynamic programming
Graphs
ISSN:0097-5397, 1095-7111
Online Access:Get full text
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Summary:We show that the treewidth and the minimum fill-in of an $n$-vertex graph can be computed in time $\mathcal{O}(1.8899^n)$. Our results are based on combinatorial proofs that an $n$-vertex graph has $\mathcal{O}(1.7087^n)$ minimal separators and $\mathcal{O}(1.8135^n)$ potential maximal cliques. We also show that for the class of asteroidal triple-free graphs the running time of our algorithms can be reduced to $\mathcal{O}(1.4142^n)$.
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ISSN:0097-5397
1095-7111
DOI:10.1137/050643350