On minimum sum of radii and diameters clustering

Authors:
Babak Behsaz;Mohammad R. Salavatipour
Affiliations:
Dept. of Computing Sci., Univ. of Alberta, Edmonton, Alberta, Canada;Dept. of Computing Sci., Univ. of Alberta, Edmonton, Alberta, Canada
Venue:
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Year:
2012

Citing 5
Cited 0

Geometric clusterings

Journal of Algorithms
Approximation algorithms for clustering to minimize the sum of diameters

Nordic Journal of Computing
Clustering to minimize the sum of cluster diameters

Journal of Computer and System Sciences - STOC 2001
On Metric Clustering to Minimize the Sum of Radii

Algorithmica - Special Issue: Scandinavian Workshop on Algorithm Theory; Guest Editor: Joachim Gudmundsson
On Clustering to Minimize the Sum of Radii

SIAM Journal on Computing

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Abstract

Given a metric (V,d) and an integer k, we consider the problem of covering the points of V with at most k clusters so as to minimize the sum of radii or the sum of diameters of these clusters. The former problem is called the Minimum Sum Radii (MSR) problem and the latter is the Minimum Sum Diameters (MSD) problem. The current best polynomial time algorithms for these problems have approximation ratios 3.504 and 7.008, respectively [2]. For the MSR problem, we give an exact algorithm when the metric is the shortest-path metric of an unweighted graph and there cannot be any singleton clusters. For the MSD problem on the plane with Euclidean distances, we present a polynomial time approximation scheme.