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.
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A preliminary version of this paper appeared in the Proceedings of the 13th Annual International Computing and Combinatorics Conference (COCOON 2007), LNCS 4598, pp. 383–393.
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Zarrabi-Zadeh, H., Chan, T.M. An Improved Algorithm for Online Unit Clustering. Algorithmica 54, 490–500 (2009). https://doi.org/10.1007/s00453-008-9208-9
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DOI: https://doi.org/10.1007/s00453-008-9208-9