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Streaming with Minimum Space: An Algorithm for Covering by Two Congruent Balls

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Combinatorial Optimization and Applications (COCOA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7402))

Abstract

In this paper we design a simple streaming algorithm for maintaining two smallest balls (of equal radius) in d-dimension to cover a set of points in an on-line fashion. Different from most of the traditional streaming models, at any step we use the minimum amount of space by only storing the locations and the (common) radius of the balls. Previously, such a geometric algorithm is only investigated for covering with one ball (one-center) by Zarrabi-Zadeh and Chan. We give an analysis of our algorithm, which is significantly different from the one-center algorithm due to the obvious possibility of grouping points wrongly under this streaming model. We obtain upper bounds of 2 and 5.708 for the case of d = 1 and d > 1 respectively. We also present some lower bounds for the corresponding problems.

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Author information

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

    Chung Keung Poon

  2. Department of Computer Science, Montana State University, Bozeman, MT, 59717, USA

    Binhai Zhu

Authors
  1. Chung Keung Poon
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  2. Binhai Zhu
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Editor information

Editors and Affiliations

  1. Department of Computing Science, University of Alberta, T6G 2E8, Edmonton, Alberta, Canada

    Guohui Lin

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© 2012 Springer-Verlag Berlin Heidelberg

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Poon, C.K., Zhu, B. (2012). Streaming with Minimum Space: An Algorithm for Covering by Two Congruent Balls. In: Lin, G. (eds) Combinatorial Optimization and Applications. COCOA 2012. Lecture Notes in Computer Science, vol 7402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31770-5_24

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  • DOI: https://doi.org/10.1007/978-3-642-31770-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31769-9

  • Online ISBN: 978-3-642-31770-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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