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Dynamic Sum-Radii Clustering

Abstract : Real networks have in common that they evolve over time and their dynamics have a huge impact on their structure. Clustering is an efficient tool to reduce the complexity to allow representation of the data. In 2014, Eisenstat et al. introduced a dynamic version of this classic problem where the distances evolve with time and where coherence over time is enforced by introducing a cost for clients to change their assigned facility. They designed a Θ(ln n)-approximation. An O(1)-approximation for the metric case was proposed later on by An et al. (2015). Both articles aimed at minimizing the sum of all client-facility distances; however, other metrics may be more relevant. In this article we aim to minimize the sum of the radii of the clusters instead. We obtain an asymptotically optimal Θ(ln n)-approximation algorithm where n is the number of clients and show that existing algorithms from An et al. (2015) do not achieve a constant approximation in the metric variant of this setting.
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https://hal.archives-ouvertes.fr/hal-01424769
Contributor : Enka Blanchard <>
Submitted on : Monday, January 2, 2017 - 6:27:10 PM
Last modification on : Wednesday, April 22, 2020 - 3:02:05 PM
Document(s) archivé(s) le : Tuesday, April 4, 2017 - 1:08:12 AM

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  • HAL Id : hal-01424769, version 1

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Nicolas Blanchard, Nicolas Schabanel. Dynamic Sum-Radii Clustering. WALCOM 2017, Mar 2017, Hsinchu, Taiwan. ⟨hal-01424769⟩

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