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Motorcycle graphs: Stochastic properties motivate an efficient yet simple implementation

Published: 26 August 2011 Publication History

Abstract

simple but very efficient algorithm for computing motorcycle graphs. An analysis of the mean trace length of n random motorcycles suggests that, on average, a motorcycle crosses only a constant number of cells within a √ n × √ n rectangular grid, provided that the motorcycles are distributed sufficiently uniformly over the area covered by the grid. This analysis motivates a simple algorithm for computing motorcycle graphs: We use the standard priority-queue--based algorithm and enhance it with geometric hashing by means of a rectangular grid. If the motorcycles are distributed sufficiently uniformly, then our stochastic analysis predicts an O(n log n) runtime. Indeed, extensive experiments run on 22,000 synthetic and real-world datasets confirm a runtime of less than 10−5 n log n seconds for the vast majority of our datasets on a standard PC. Further experiments with our software, Moca, also confirm the mean trace length and average number of cells crossed by a motorcycle, as predicted by our analysis. This makes Moca the first implementation that is efficient enough to be applied in practice for computing motorcycle graphs of large datasets. Actually, it is easy to extend Moca to make it compute a generalized version of the original motorcycle graph, thus enabling a significantly larger field of applications.

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Cited By

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  • (2022)Incremental Construction of Motorcycle GraphsAlgorithms10.3390/a1507022515:7(225)Online publication date: 27-Jun-2022
  • (2018)A Faster Algorithm for Computing Motorcycle GraphsDiscrete & Computational Geometry10.1007/s00454-014-9625-252:3(492-514)Online publication date: 31-Dec-2018
  • (2012)A FAST STRAIGHT-SKELETON ALGORITHM BASED ON GENERALIZED MOTORCYCLE GRAPHSInternational Journal of Computational Geometry & Applications10.1142/S021819591250012422:05(471-498)Online publication date: Oct-2012

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  1. Motorcycle graphs: Stochastic properties motivate an efficient yet simple implementation

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    cover image ACM Journal of Experimental Algorithmics
    ACM Journal of Experimental Algorithmics  Volume 16, Issue
    2011
    411 pages
    ISSN:1084-6654
    EISSN:1084-6654
    DOI:10.1145/1963190
    Issue’s Table of Contents
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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 26 August 2011
    Published in JEA Volume 16

    Author Tags

    1. Geometric hashing
    2. motorcycle graph
    3. stochastic analysis

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    Cited By

    View all
    • (2022)Incremental Construction of Motorcycle GraphsAlgorithms10.3390/a1507022515:7(225)Online publication date: 27-Jun-2022
    • (2018)A Faster Algorithm for Computing Motorcycle GraphsDiscrete & Computational Geometry10.1007/s00454-014-9625-252:3(492-514)Online publication date: 31-Dec-2018
    • (2012)A FAST STRAIGHT-SKELETON ALGORITHM BASED ON GENERALIZED MOTORCYCLE GRAPHSInternational Journal of Computational Geometry & Applications10.1142/S021819591250012422:05(471-498)Online publication date: Oct-2012

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