A Note on Minimum-Sum Coverage by Aligned Disks
Computational Geometry
2012-07-03 v3
Abstract
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 a form of a non-decreasing function f(r) = r^a for any a >= 1. The goal is to find a set of disks under Lp metric such that the disks are centered on the x-axis, their union covers n points, and the sum of the cost of the disks is minimized. Alt et al. [1] presented an algorithm in O(n^4 log n) time for any a > 1 under any Lp metric. We present a faster algorithm for this problem in O(n^2 log n) time for any a > 1 and any Lp metric.
Keywords
Cite
@article{arxiv.1202.4821,
title = {A Note on Minimum-Sum Coverage by Aligned Disks},
author = {Chan-Su Shin},
journal= {arXiv preprint arXiv:1202.4821},
year = {2012}
}
Comments
7 pages, 1 figure