License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2016.4
URN: urn:nbn:de:0030-drops-67742
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6774/
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Abu-Khzam, Faisal ; Bazgan, Cristina ; Casel, Katrin ; Fernau, Henning

Building Clusters with Lower-Bounded Sizes

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Abstract

Classical clustering problems search for a partition of objects into a fixed number of clusters. In many scenarios however the number of clusters is not known or necessarily fixed. Further, clusters are sometimes only considered to be of significance if they have a certain size. We discuss clustering into sets of minimum cardinality k without a fixed number of sets and present a general model for these types of problems. This general framework allows the comparison of different measures to assess the quality of a clustering. We specifically consider nine quality-measures and classify the complexity of the resulting problems with respect to k. Further, we derive some polynomial-time solvable cases for k = 2 with connections to matching-type problems which, among other graph problems, then are used to compute approximations for larger values of k.

BibTeX - Entry

@InProceedings{abukhzam_et_al:LIPIcs:2016:6774,
  author =	{Faisal Abu-Khzam and Cristina Bazgan and Katrin Casel and Henning Fernau},
  title =	{{Building Clusters with Lower-Bounded Sizes}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6774},
  URN =		{urn:nbn:de:0030-drops-67742},
  doi =		{10.4230/LIPIcs.ISAAC.2016.4},
  annote =	{Keywords: Clustering, Approximation Algorithms, Complexity, Matching}
}

Keywords: Clustering, Approximation Algorithms, Complexity, Matching
Collection: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 07.12.2016

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