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A Randomized Algorithm for Online Unit Clustering

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Approximation and Online Algorithms (WAOA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4368))

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Abstract

In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used. In the one-dimensional case, we show that surprisingly the naïve upper bound of 2 on the competitive ratio can be beaten: we present a new randomized 15/8-competitive online algorithm. We also provide some lower bounds and an extension to higher dimensions.

Work of the first author has been supported in part by NSERC.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Timothy M. Chan & Hamid Zarrabi-Zadeh

Authors
  1. Timothy M. Chan
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  2. Hamid Zarrabi-Zadeh
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

  2. Research Academic Computer Technology Institute &, Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Greece

    Christos Kaklamanis

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© 2007 Springer-Verlag Berlin Heidelberg

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Chan, T.M., Zarrabi-Zadeh, H. (2007). A Randomized Algorithm for Online Unit Clustering. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_10

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  • DOI: https://doi.org/10.1007/11970125_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69513-4

  • Online ISBN: 978-3-540-69514-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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