On the online unit clustering problem

Authors:
Leah Epstein;Rob Van Stee
Affiliations:
Department of Mathematics, University of Haifa, Haifa, Israel;Department of Computer Science, University of Karlsruhe, Karlsruhe, Germany
Venue:
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Year:
2007

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Abstract

We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh (Proc. Workshop on Approximation and Online Algorithms 2006, LNCS 4368, p. 121-131. Springer, 2006). We design a deterministic algorithm with a competitive ratio of 7/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2. It also has a better competitive ratio than the previous randomized algorithm. Moreover, we provide the first non-trivial deterministic lower bound, improve the randomized lower bound, and prove the first lower bounds for higher dimensions.