Planar Separators and Parallel Polygon Triangulation

We show how to construct an O(√ n)-separator decomposition of a planar graph G in O( n) time. Such a decomposition defines a binary tree, where each node corresponds to a subgraph of G and stores an O(√ n)-separator of that subgraph. We also show how to construct an O( n ϵ)-way decomposition tree in...

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Bibliographic Details
Published inJournal of computer and system sciences Vol. 51; no. 3; pp. 374 - 389
Main Author Goodrich, M.T.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Brugge Elsevier Inc 01.12.1995
Academic Press
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Information retrieval. Graph
Theoretical computing
Design
Graph decomposition
Parallel algorithm
Triangulation
Planar graph
Subgraph
Separator
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Summary:We show how to construct an O(√ n)-separator decomposition of a planar graph G in O( n) time. Such a decomposition defines a binary tree, where each node corresponds to a subgraph of G and stores an O(√ n)-separator of that subgraph. We also show how to construct an O( n ϵ)-way decomposition tree in parallel in O(log n) time so that each node corresponds to a subgraph of G and stores an O( n 12+ϵ)-separator of that subgraph. We demonstrate the utility of such a separator decomposition by showing how it can be used in the design of a parallel algorithm for triangulating a simple polygon deterministically in O(log n) time using O( n/log n) processors on a CRCW PRAM.
ISSN:0022-0000
1090-2724
DOI:10.1006/jcss.1995.1076