Computing k-center over Streaming Data for Small k

  • Hee-Kap Ahn
  • Hyo-Sil Kim
  • Sang-Sub Kim
  • Wanbin Son
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)


The Euclidean k-center problem is to compute k congruent balls covering a given set of points in ℝ d such that the radius is minimized. We consider the k-center problem in ℝ d for k = 2,3 in a single-pass streaming model, where data is allowed to be examined once and only a small amount of information can be stored in a device. We present two approximation algorithms whose space complexity does not depend on the size of the input data. The first algorithm guarantees a (2 + ε)-factor using O(d/ε) space in arbitrary dimensions, and the second algorithm guarantees a (1 + ε)-factor using O(1/ε d ) space in constant dimensions. The same algorithms can be used to compute a k-center under any L p metric for k = 2,3.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Hyo-Sil Kim
    • 1
  • Sang-Sub Kim
    • 1
  • Wanbin Son
    • 1
  1. 1.Pohang University of Science and TechnologyKorea

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