Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Approximations and optimal geometric divide-and-conquer
Selected papers of the 23rd annual ACM symposium on Theory of computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
An Expander-Based Approach to Geometric Optimization
SIAM Journal on Computing
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Translating a Planar Object to Maximize Point Containment
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Translating a regular grid over a point set
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
On approximating the depth and related problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Covering point sets with two disjoint disks or squares
Computational Geometry: Theory and Applications
Covering point sets with two disjoint disks or squares
Computational Geometry: Theory and Applications
Survey: Covering problems in facility location: A review
Computers and Industrial Engineering
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Let P be a set of n weighted points. We study approximation algorithms for the following two continuous facility-location problems. In the first problem we want to place m unit disks, for a given constant m≥1, such that the total weight of the points from P inside the union of the disks is maximized. We present a deterministic algorithm that can compute, for any ε0, a (1−ε)-approximation to the optimal solution in O(n logn + ε$^{{\rm -4}{\it m}}$log$^{\rm 2{\it m}}$ (1/ε)) time. In the second problem we want to place a single disk with center in a given constant-complexity region X such that the total weight of the points from P inside the disk is minimized. Here we present an algorithm that can compute, for any ε0, with high probability a (1+ε)-approximation to the optimal solution in O(n (log3n + ε−4 log2n )) expected time.