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dc.contributor.authorHøgemo, Svein
dc.contributor.authorPaul, Christophe
dc.contributor.authorTelle, Jan Arne
dc.date.accessioned2021-07-02T08:15:51Z
dc.date.available2021-07-02T08:15:51Z
dc.date.created2020-09-22T16:24:36Z
dc.date.issued2020
dc.PublishedLeibniz International Proceedings in Informatics. 2020, 170:47 1-13.
dc.identifier.issn1868-8969
dc.identifier.urihttps://hdl.handle.net/11250/2763037
dc.description.abstractWe study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that takes any such clustering of a graph G and iteratively improves it until a desired target clustering of G is reached. We use this technique to show both a negative and a positive complexity result. Firstly, we show that in general the problem is NP-complete. Secondly, we consider min-well-behaved graphs, which are graphs H having the property that for any k the graph H^{(k)} being the join of k copies of H has an optimal hierarchical clustering that splits each copy of H in the same optimal way. To optimally cluster such a graph H^{(k)} we thus only need to optimally cluster the smaller graph H. Co-bipartite graphs are min-well-behaved, but otherwise they seem to be scarce. We use the normalization procedure to show that also the cycle on 6 vertices is min-well-behaved.en_US
dc.language.isoengen_US
dc.publisherDagstuhl publishingen_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.no*
dc.titleHierarchical clusterings of unweighted graphsen_US
dc.typeJournal articleen_US
dc.typePeer revieweden_US
dc.description.versionpublishedVersionen_US
dc.rights.holderCopyright 2020 The Authorsen_US
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode1
dc.identifier.doi10.4230/LIPIcs.MFCS.2020.47
dc.identifier.cristin1832255
dc.source.journalLeibniz International Proceedings in Informaticsen_US
dc.source.40170:47
dc.source.pagenumber1-13en_US
dc.identifier.citationLeibniz International Proceedings in Informatics. 2020, 47, 1-13en_US
dc.source.volume47en_US


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