Abstract
We present a single-pass, (1.8 + ε)-factor, O(1/ε)-space data stream algorithm for the Euclidean 2-center problem for any fixed d ≥ 1. This is an improvement on the approximation factor over the (2 + ε)-factor and O(1/ε)-space algorithms of Ahn et al. [3] and Guha [8]. It can also be considered as an improvement on the space over the (1 + ε)-factor and O(1/ε d)-space algorithm of Zarrabi-Zadeh [11], while sacrificing the approximation factor a little bit. To our best knowledge, this is the first breakthrough with an approximation factor below 2 using O(1/ε) space for any fixed d. Our algorithm also extends to the k-center problem with k > 2.
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2011-0030044).
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Kim, SS., Ahn, HK. (2014). An Improved Data Stream Algorithm for Clustering. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_24
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DOI: https://doi.org/10.1007/978-3-642-54423-1_24
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