Competitive Strategies for Online Clique Clustering

  • Marek Chrobak
  • Christoph Dürr
  • Bengt J. Nilsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9079)

Abstract

A clique clustering of a graph is a partitioning of its vertices into disjoint cliques. The quality of a clique clustering is measured by the total number of edges in its cliques. We consider the online variant of the clique clustering problem, where the vertices of the input graph arrive one at a time. At each step, the newly arrived vertex forms a singleton clique, and the algorithm can merge any existing cliques in its partitioning into larger cliques, but splitting cliques is not allowed. We give an online strategy with competitive ratio \(15.645\) and we prove a lower bound of \(6\) on the competitive ratio, improving the previous respective bounds of \(31\) and \(2\).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marek Chrobak
    • 1
  • Christoph Dürr
    • 2
    • 3
  • Bengt J. Nilsson
    • 4
  1. 1.University of California at RiversideRiversideUSA
  2. 2.Sorbonne UniversitésUPMC Univ Paris 06, UMR 7606, LIP6ParisFrance
  3. 3.CNRSUMR 7606, LIP6ParisFrance
  4. 4.Department of Computer ScienceMalmö UniversityMalmöSweden

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