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Optimal Embedding into Star Metrics

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Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

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Abstract

We present an O(n 3 log2 n)-time algorithm for the following problem: given a finite metric space X, create a star-topology network with the points of X as its leaves, such that the distances in the star are at least as large as in X, with minimum dilation. As part of our algorithm, we solve in the same time bound the parametric negative cycle detection problem: given a directed graph with edge weights that are increasing linear functions of a parameter λ, find the smallest value of λ such that the graph contains no negative-weight cycles.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Universitiy of California, Irvine, USA

    David Eppstein & Kevin A. Wortman

Authors
  1. David Eppstein
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  2. Kevin A. Wortman
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

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Eppstein, D., Wortman, K.A. (2009). Optimal Embedding into Star Metrics. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_26

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  • DOI: https://doi.org/10.1007/978-3-642-03367-4_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03366-7

  • Online ISBN: 978-3-642-03367-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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