Abstract
Given a data set in metric space, we study the problem of hierarchical clustering to minimize the maximum cluster diameter, and the hierarchical k-supplier problem with customers arriving online.
We prove that two previously known algorithms for hierarchical clustering, one (offline) due to Dasgupta and Long and the other (online) due to Charikar, Chekuri, Feder and Motwani, are essentially the same algorithm when points are considered in the same order. We show that the analysis of both algorithms are tight and exhibit a new lower bound for hierarchical clustering. Finally we present the first constant factor approximation algorithm for the online hierarchical k-supplier problem.
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Das, A., Kenyon, C. (2007). On Hierarchical Diameter-Clustering, and the Supplier Problem. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_11
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DOI: https://doi.org/10.1007/11970125_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69513-4
Online ISBN: 978-3-540-69514-1
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