Theory of Computing Systems

, Volume 45, Issue 3, pp 486–496 | Cite as

A Randomized Algorithm for Online Unit Clustering

  • Timothy M. Chan
  • Hamid Zarrabi-Zadeh


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.


Online algorithms Randomized algorithms Unit clustering 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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