Online Sum-Radii Clustering

Fotakis, D; Koutris, P

dc.contributor.author	Fotakis, D	en
dc.contributor.author	Koutris, P	en
dc.date.accessioned	2014-03-01T02:53:59Z
dc.date.available	2014-03-01T02:53:59Z
dc.date.issued	2012	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/36510
dc.subject.other	Competitive algorithms	en
dc.subject.other	Competitive ratio	en
dc.subject.other	Euclidean planes	en
dc.subject.other	Lower bounds	en
dc.subject.other	Metric spaces	en
dc.subject.other	On-line algorithms	en
dc.subject.other	Primal-dual	en
dc.subject.other	Total costs	en
dc.subject.other	Tree metrics	en
dc.subject.other	Upper Bound	en
dc.subject.other	Computer science	en
dc.subject.other	Costs	en
dc.subject.other	Forestry	en
dc.subject.other	Trees (mathematics)	en
dc.subject.other	Clustering algorithms	en
dc.subject.other	Algorithms	en
dc.subject.other	Computers	en
dc.subject.other	Costs	en
dc.subject.other	Forestry	en
dc.subject.other	Mathematics	en
dc.subject.other	Trees	en
dc.title	Online Sum-Radii Clustering	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-32589-2_36	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-32589-2_36	en
heal.publicationDate	2012	en
heal.abstract	In Online Sum-Radii Clustering, n demand points arrive online and must be irrevocably assigned to a cluster upon arrival. The cost of each cluster is the sum of a fixed opening cost and its radius, and the objective is to minimize the total cost of the clusters opened by the algorithm. We show that the deterministic competitive ratio of Online Sum-Radii Clustering for general metric spaces is Θ(logn), where the upper bound follows from a primal-dual online algorithm, and the lower bound is valid for ternary Hierarchically Well-Separated Trees (HSTs) and for the Euclidean plane. Combined with the results of (Csirik et al., MFCS 2010), this result demonstrates that the deterministic competitive ratio of Online Sum-Radii Clustering changes abruptly, from constant to logarithmic, when we move from the line to the plane. We also show that Online Sum-Radii Clustering in HSTs is closely related to the Parking Permit problem introduced by (Meyerson, FOCS 2005). Exploiting the relation to Parking Permit, we obtain a lower bound of Ω(loglogn) on the randomized competitive ratio of Online Sum-Radii Clustering in tree metrics. Moreover, we present a simple randomized O(logn)-competitive algorithm, and a deterministic O(loglogn)-competitive algorithm for the fractional version of the problem. © 2012 Springer-Verlag.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-642-32589-2_36	en
dc.identifier.volume	7464 LNCS	en
dc.identifier.spage	395	en
dc.identifier.epage	406	en