eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-07
4:1
4:13
10.4230/LIPIcs.ISAAC.2016.4
article
Building Clusters with Lower-Bounded Sizes
Abu-Khzam, Faisal
Bazgan, Cristina
Casel, Katrin
Fernau, Henning
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol064-isaac2016/LIPIcs.ISAAC.2016.4/LIPIcs.ISAAC.2016.4.pdf
Clustering
Approximation Algorithms
Complexity
Matching