A Randomized Algorithm for Online Unit Clustering

Authors:
Timothy M. Chan;Hamid Zarrabi-Zadeh
Affiliations:
University of Waterloo, School of Computer Science, N2L 3G1, Waterloo, ON, Canada;University of Waterloo, School of Computer Science, N2L 3G1, Waterloo, ON, Canada
Venue:
Theory of Computing Systems
Year:
2009

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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.