SIAM Journal on Computing
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
Approximation algorithms for clustering to minimize the sum of diameters
Nordic Journal of Computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Clustering to minimize the sum of cluster diameters
Journal of Computer and System Sciences - STOC 2001
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
How much precision is needed to compare two sums of square roots of integers?
Information Processing Letters
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
On Metric Clustering to Minimize the Sum of Radii
Algorithmica - Special Issue: Scandinavian Workshop on Algorithm Theory; Guest Editor: Joachim Gudmundsson
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Partitioning the nodes of a graph to minimize the sum of subgraph radii
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
On minimum sum of radii and diameters clustering
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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Let $P$ be a set of $n$ points in the plane. Consider the problem of finding $k$ disks, each centered at a point in $P$, whose union covers $P$ with the objective of minimizing the sum of the radii of the disks. We present an exact algorithm for this well-studied problem with polynomial running time, under the assumption that two candidate solutions can be compared efficiently. The algorithm generalizes in a straightforward manner to any fixed dimension and to some other related problems.