Enclosing weighted points with an almost-unit ball
Information Processing Letters
A scalable algorithm for maximizing range sum in spatial databases
Proceedings of the VLDB Endowment
Covering a bichromatic point set with two disjoint monochromatic disks
Computational Geometry: Theory and Applications
Approximate MaxRS in spatial databases
Proceedings of the VLDB Endowment
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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 algorithms that compute, for any fixed ε0, a (1−ε)-approximation to the optimal solution in O(nlog n) 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 computes, for any fixed ε0, in O(nlog 2 n) expected time a disk that is, with high probability, a (1+ε)-approximation to the optimal solution.