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.
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Epstein, L., van Stee, R. (2008). On the Online Unit Clustering Problem. In: Kaklamanis, C., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2007. Lecture Notes in Computer Science, vol 4927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77918-6_16
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DOI: https://doi.org/10.1007/978-3-540-77918-6_16
Publisher Name: Springer, Berlin, Heidelberg
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