Planar geometric location problems

Pankaj K. Agarwal; Micha Sharir

doi:10.1007/BF01182774

Planar geometric location problems

Pankaj K. Agarwal^*
, Micha Sharir

^*Corresponding author for this work

School of Computer Science and AI

Duke University
New York University

Research output: Contribution to journal › Article › peer-review

60 Scopus citations

Abstract

We present an O(n² log³n) algorithm for the two-center problem, in which we are given a set S of n points in the plane and wish to find two closed disks whose union contains S so that the larger of the two radii is as small as possible. We also give an O(n² log⁵n) algorithm for solving the two-line-center problem, where we want to find two strips that cover S whose maximum width is as small as possible. The best previous solutions of both problems require O(n³) time.

Original language	English
Pages (from-to)	185-195
Number of pages	11
Journal	Algorithmica
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/BF01182774
State	Published - Feb 1994

Keywords

Duality
Facility location
Parametric searching
Planar arrangements

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10.1007/BF01182774

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KW - Duality

KW - Facility location

KW - Parametric searching

KW - Planar arrangements

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Planar geometric location problems

Abstract

Keywords

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