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Partitioning planar graphs with costs and weights

Published: 09 February 2007 Publication History

Abstract

A graph separator is a set of vertices or edges whose removal divides an input graph into components of bounded size. This paper describes new algorithms for computing separators in planar graphs as well as techniques that can be used to speed up the implementation of graph partitioning algorithms and improve the partition quality. In particular, we consider planar graphs with costs and weights on the vertices, where weights are used to estimate the sizes of the partitions and costs are used to estimate the size of the separator. We show that in these graphs one can always find a small cost separator (consisting of vertices or edges) that partitions the graph into components of bounded weight. We describe implementations of the partitioning algorithms and discuss results of our experiments.

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Cited By

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  • (2016)Short and Simple Cycle Separators in Planar GraphsACM Journal of Experimental Algorithmics10.1145/295731821(1-24)Online publication date: 15-Sep-2016
  • (2013)Structured recursive separator decompositions for planar graphs in linear timeProceedings of the forty-fifth annual ACM symposium on Theory of Computing10.1145/2488608.2488672(505-514)Online publication date: 1-Jun-2013
  • (2010)Engineering planar separator algorithmsACM Journal of Experimental Algorithmics10.1145/1498698.157163514(1.5-1.31)Online publication date: 5-Jan-2010
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  1. Partitioning planar graphs with costs and weights

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    Published In

    cover image ACM Journal of Experimental Algorithmics
    ACM Journal of Experimental Algorithmics  Volume 11, Issue
    2006
    355 pages
    ISSN:1084-6654
    EISSN:1084-6654
    DOI:10.1145/1187436
    Issue’s Table of Contents

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 09 February 2007
    Published in JEA Volume 11

    Author Tags

    1. Graph algorithms
    2. graph partitioning algorithms
    3. graph separators
    4. implementation

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    Cited By

    View all
    • (2016)Short and Simple Cycle Separators in Planar GraphsACM Journal of Experimental Algorithmics10.1145/295731821(1-24)Online publication date: 15-Sep-2016
    • (2013)Structured recursive separator decompositions for planar graphs in linear timeProceedings of the forty-fifth annual ACM symposium on Theory of Computing10.1145/2488608.2488672(505-514)Online publication date: 1-Jun-2013
    • (2010)Engineering planar separator algorithmsACM Journal of Experimental Algorithmics10.1145/1498698.157163514(1.5-1.31)Online publication date: 5-Jan-2010
    • (2009)A linear-time algorithm to find a separator in a graph excluding a minorACM Transactions on Algorithms10.1145/1597036.15970435:4(1-16)Online publication date: 6-Nov-2009
    • (2009)Throughput-driven synthesis of embedded software for pipelined execution on multicore architecturesACM Transactions on Embedded Computing Systems10.1145/1457255.14572588:2(1-35)Online publication date: 9-Feb-2009
    • (2009)Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral SurfacesDiscrete & Computational Geometry10.1007/s00454-009-9204-044:4(762-801)Online publication date: 7-Jul-2009

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