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Clustering with Lower-Bounded Sizes - A General Graph-Theoretic Framework

Abu-Khzam, Faisal N.; Bazgan, Cristina; Casel, Katrin; Fernau, Henning (2018), Clustering with Lower-Bounded Sizes - A General Graph-Theoretic Framework, Algorithmica, 80, 9, p. 2517-2550. 10.1007/s00453-017-0374-5

Type
Article accepté pour publication ou publié
Date
2018
Journal name
Algorithmica
Volume
80
Number
9
Publisher
Springer
Pages
2517-2550
Publication identifier
Metadata
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Author(s)
Abu-Khzam, Faisal N.

Bazgan, Cristina
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Casel, Katrin
Theoretical Computer Science, University of Trier, Germany
Fernau, Henning
Theoretical Computer Science, University of Trier, Germany
Abstract (EN)
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.
Subjects / Keywords
Clustering; Computational complexity; Approximation algorithms; Anonymisation