research-article

Applications of a Planar Separator Theorem

Authors:

Richard J. Lipton,

Robert Endre TarjanAuthors Info & Claims

SIAM Journal on Computing, Volume 9, Issue 3

Pages 615 - 627

https://doi.org/10.1137/0209046

Published: 01 August 1980 Publication History

Abstract

Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only $O(\sqrt n )$ vertices. This separator theorem, in combination with a divide-and-conquer strategy, leads to many new complexity results for planar graph problems. This paper describes some of these results.

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Index Terms

Applications of a Planar Separator Theorem
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
2. Theory of computation

Index terms have been assigned to the content through auto-classification.

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Published In

cover image SIAM Journal on Computing

SIAM Journal on Computing Volume 9, Issue 3

Aug 1980

224 pages

ISSN:0097-5397

DOI:10.1137/smjcat.1980.9.issue-3

Issue’s Table of Contents

Copyright © 1980 Society for Industrial and Applied Mathematics.

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 August 1980

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Cited By

Abo Khamis MNgo HPichler RSuciu DWang Y(2024)Convergence of datalog over (Pre-) SemiringsJournal of the ACM10.1145/364302771:2(1-55)Online publication date: 10-Apr-2024
https://dl.acm.org/doi/10.1145/3643027
Le HThan C(2024)Greedy Spanners in Euclidean Spaces Admit Sublinear SeparatorsACM Transactions on Algorithms10.1145/359077120:3(1-30)Online publication date: 21-Jun-2024
https://dl.acm.org/doi/10.1145/3590771
Pan JWang JLi G(2024)Survey of vector database management systemsThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-024-00864-x33:5(1591-1615)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s00778-024-00864-x
Romero MWrochna MŽivný S(2023)Pliability and Approximating Max-CSPsJournal of the ACM10.1145/362651570:6(1-43)Online publication date: 30-Nov-2023
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Abo Khamis MNgo HPichler RSuciu DRemy Wang Y(2023)Convergence of Datalog over (Pre-) SemiringsACM SIGMOD Record10.1145/3604437.360445452:1(75-82)Online publication date: 8-Jun-2023
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Bonnet ÉCabello SMulzer W(2023)Maximum Matchings in Geometric Intersection GraphsDiscrete & Computational Geometry10.1007/s00454-023-00564-370:3(550-579)Online publication date: 9-Sep-2023
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