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
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks and ISDN Systems
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
On clustering to minimize the sum of radii
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On clustering to minimize the sum of radii
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On Metric Clustering to Minimize the Sum of Radii
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
The Planar k-Means Problem is NP-Hard
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Cheap or Flexible Sensor Coverage
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
The structural clustering and analysis of metric based on granular space
Pattern Recognition
Multi cover of a polygon minimizing the sum of areas
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Topology construction for rural wireless mesh networks - a geometric approach
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Connecting a set of circles with minimum sum of radii
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The planar k-means problem is NP-hard
Theoretical Computer Science
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
ACM Transactions on Sensor Networks (TOSN)
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Given a metric d defined on a set V of points (a metric space), we define the ball B(v, r) centered at u ∈ V and having radius r ≥ 0 to be the set {q ∈ V/d(v, q) ≤r}. In this work, we consider the problem of computing a minimum cost k-cover for a given set P ⊆ V of n points, where k 0 is some given integer which is also part of the input. For k ≥ 0, a k-cover for subset Q ⊆ P is a set of at most k balls, each centered at a point in P, whose union covers (contains) Q. The cost of a set D of balls, denoted cost(D), is the sum of the radii of those balls.