Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Connecting a set of circles with minimum sum of radii
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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In this paper, we consider a facility location problem to find a minimum-sum coverage of n points by disks centered at a fixed line. The cost of a disk with radius r has the form of a nondecreasing function f(r)=r^@a for any @a=1. The goal is to find a set of disks in any L"p-metric such that the disks are centered on the x-axis, their union covers the points, and the sum of the cost of the disks is minimized. Alt et al. [1] presented an algorithm running in O(n^4logn) time for any @a1 in any L"p-metric. We present a faster algorithm that runs in O(n^2logn) time for any @a1 and any L"p-metric.