An Improved Algorithm for Online Unit Clustering

Authors:
Hamid Zarrabi-Zadeh;Timothy M. Chan
Affiliations:
University of Waterloo, School of Computer Science, Waterloo, Ontario, Canada;University of Waterloo, School of Computer Science, Waterloo, Ontario, Canada
Venue:
Algorithmica
Year:
2009

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Abstract

We revisit the online unit clustering problem in one dimension which we recently introduced at WAOA’06: given a sequence of n points on the line, the objective is to partition the points into a minimum number of subsets, each enclosable by a unit interval. We present a new randomized online algorithm that achieves expected competitive ratio 11/6 against oblivious adversaries, improving the previous ratio of 15/8. This immediately leads to improved upper bounds for the problem in two and higher dimensions as well.