A fully polynomial time approximation scheme for the smallest diameter of imprecise points

Given a set D={d1,…,dn} of imprecise points modeled as disks, the minimum diameter problem is to locate a set P={p1,…,pn} of fixed points, where pi∈di, such that the furthest distance between any pair of points in P is as small as possible. This introduces a tight lower bound on the size of the diam...

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Bibliographic Details
Published inTheoretical computer science Vol. 814; pp. 259 - 270
Main Authors Keikha, Vahideh, Löffler, Maarten, Mohades, Ali
Format Journal Article
LanguageEnglish
Published Elsevier B.V 24.04.2020
Subjects
Approximation algorithms
Computational geometry
Imprecise points
Minimum diameter
Imprecise points
Computational geometry
Minimum diameter
Approximation algorithms
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ISSN0304-3975
1879-2294
DOI10.1016/j.tcs.2020.02.006

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Summary:Given a set D={d1,…,dn} of imprecise points modeled as disks, the minimum diameter problem is to locate a set P={p1,…,pn} of fixed points, where pi∈di, such that the furthest distance between any pair of points in P is as small as possible. This introduces a tight lower bound on the size of the diameter of any instance P. In this paper, we present a fully polynomial time approximation scheme (FPTAS) for computing the minimum diameter of a set of disjoint disks that runs in O(n2ϵ−1) time. Then we relax the disjointness assumption and we show that adjusting the presented FPTAS will cost O(n2ϵ−2) time. We also show that our results can be generalized in Rd when the dimension d is an arbitrary fixed constant.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2020.02.006