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Dynamic Sum-Radii Clustering

  • Nicolas K. Blanchard
  • Nicolas Schabanel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10167)

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 \(\varTheta (\ln n)\)-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 \(\varTheta (\ln n)\)-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.

Keywords

Facility location Approximation algorithms Clustering Dynamic graphs 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.U. Paris DiderotParisFrance
  2. 2.ENS ParisParisFrance
  3. 3.CNRS, U. Paris DiderotParisFrance
  4. 4.IXXI, U. LyonParisFrance

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