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• W1567158140 abstract "In this paper we consider several instances of the k-center on a line problem where the goal is, given a set of points S in the plane and a parameter k >= 1, to find k disks with centers on a line l such that their union covers S and the maximum radius of the disks is minimized. This problem is a constraint version of the well-known k-center problem in which the centers are constrained to lie in a particular region such as a segment, a line, and a polygon. We first consider the simplest version of the problem where the line l is given in advance; we can solve this problem in O(n log^2 n) time. We then investigate the cases where only the orientation of the line l is fixed and where the line l can be arbitrary. We can solve these problems in O(n^2 log^2 n) time and in O(n^4 log^2 n) expected time, respectively. For the last two problems, we present (1 + e)-approximation algorithms, which run in O((1/e) n log^2 n) time and O((1/e^2) n log^2 n) time, respectively." @default.
• W1567158140 created "2016-06-24" @default.
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• W1567158140 date "2009-02-19" @default.
• W1567158140 modified "2023-09-23" @default.
• W1567158140 title "Computing k-Centers On a Line" @default.
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