Treffer: On the Online Unit Clustering Problem.

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. [ABSTRACT FROM AUTHOR]

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