Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Clustering to minimize the sum of cluster diameters
Journal of Computer and System Sciences - STOC 2001
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
On the set multi-cover problem in geometric settings
Proceedings of the twenty-fifth annual symposium on Computational geometry
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling
Proceedings of the twenty-third 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
A note on multicovering with disks
Computational Geometry: Theory and Applications
Weighted geometric set multi-cover via quasi-uniform sampling
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider variants of the following multi-covering problem with disks. We are given two point sets Y (servers) and X (clients) in the plane, and a coverage function κ :X - N. Centered at each server is a single disk whose radius we are free to set. The requirement is that each client x ∈ X be covered by at least κ(x) of the server disks. The objective function we wish to minimize is the sum of the areas of the disks. We present a polynomial time algorithm for this problem achieving an O(1) approximation.