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A Parallel Approximation Algorithm for Minimum Weight Triangulation

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1530))

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Abstract

We show a parallel algorithm that produces a triangulation which is within a constant factor longer than the Minimum Weight Triangulation (MWT) in time O(logn) using O(n) processors and linear space in the CRCW PRAM model. This is done by developing a relaxed version of the quasi-greedy triangulation algorithm. The relaxed version produces edges that are at most (1+ε) longer than the shortest diagonal, where ε is some positive constant smaller than 1, still outputs a triangulation which is within a constant factor longer that the minimum weight triangulation. However, if the same method is applied to the straight-forward greedy algorithm the approximation behavior may deteriorate dramatically, i.e. Ω(n) longer than a minimum weight triangulation, if the lengths of the edges are not computed with high precision.

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Authors and Affiliations

  1. Department of Computer Science, Lund University, Box 118, S-221 00, Lund, Sweden

    Joachim Gudmundsson & Christos Levcopoulos

Authors
  1. Joachim Gudmundsson
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  2. Christos Levcopoulos
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Editors and Affiliations

  1. The Institute of Mathematical Sciences, 600 113, Chennai, India

    Vikraman Arvind

  2. National Institute of Advanced Studies, Indian Institute of Science Campus, 560012, Bangalore, India

    Sundar Ramanujam

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© 1998 Springer-Verlag Berlin Heidelberg

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Gudmundsson, J., Levcopoulos, C. (1998). A Parallel Approximation Algorithm for Minimum Weight Triangulation. In: Arvind, V., Ramanujam, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1998. Lecture Notes in Computer Science, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49382-2_21

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  • DOI: https://doi.org/10.1007/978-3-540-49382-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65384-4

  • Online ISBN: 978-3-540-49382-2

  • eBook Packages: Springer Book Archive

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