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On Hierarchical Diameter-Clustering and the Supplier Problem

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Abstract

Given a data set in a 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, output essentially the same result when points are considered in the same order. We show that the analyses 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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Authors and Affiliations

  1. Brown University, Providence, RI, 02918, USA

    Aparna Das & Claire Kenyon-Mathieu

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  1. Aparna Das
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  2. Claire Kenyon-Mathieu
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Correspondence to Aparna Das.

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Das, A., Kenyon-Mathieu, C. On Hierarchical Diameter-Clustering and the Supplier Problem. Theory Comput Syst 45, 497–511 (2009). https://doi.org/10.1007/s00224-009-9186-6

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  • DOI: https://doi.org/10.1007/s00224-009-9186-6

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