Treewidth and minimum fill-in on permutation graphs in linear time
Permutation graphs form a well-studied subclass of cocomparability graphs. Permutation graphs are the cocomparability graphs whose complements are also cocomparability graphs. A triangulation of a graph G is a graph H that is obtained by adding edges to G to make it chordal. If no triangulation of...
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Published in | Theoretical computer science Vol. 411; no. 40; pp. 3685 - 3700 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Oxford
Elsevier B.V
06.09.2010
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | Permutation graphs form a well-studied subclass of cocomparability graphs. Permutation graphs are the cocomparability graphs whose complements are also cocomparability graphs. A triangulation of a graph
G
is a graph
H
that is obtained by adding edges to
G
to make it chordal. If no triangulation of
G
is a proper subgraph of
H
then
H
is called a minimal triangulation. The main theoretical result of the paper is a characterisation of the minimal triangulations of a permutation graph, that also leads to a succinct and linear-time computable representation of the set of minimal triangulations. We apply this representation to devise linear-time algorithms for various minimal triangulation problems on permutation graphs, in particular, we give linear-time algorithms for computing treewidth and minimum fill-in on permutation graphs. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0304-3975 1879-2294 |
DOI: | 10.1016/j.tcs.2010.06.017 |