Planar geometric location problems and maintaining the width of a planar set

Pankaj K. Agarwal, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present an O(n2 log3 n) algorithm for the two-center problem, in which we are given a set 5 of n points in the plane and wish to find two closed discs whose union contains S so that the larger of the two radii is as small as possible. We also give an O(n2 log5 n) 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. To obtain the second result, we need as a subroutine an algorithm for determining whether the width of a given set S of points in the plane ever becomes less than or equal to a given parameter W > 0, as we perform n insertions and deletions on S, and the sequence of these operations is known in advance. We present an O(n log3 n) algorithm for solving this problem.

Original languageEnglish
Title of host publicationProceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991
PublisherAssociation for Computing Machinery
Pages449-458
Number of pages10
ISBN (Print)0897913760
StatePublished - 1 Mar 1991
Event2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 - San Francisco, United States
Duration: 28 Jan 199130 Jan 1991

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991
Country/TerritoryUnited States
CitySan Francisco
Period28/01/9130/01/91

Funding

FundersFunder number
Israeli Academy of Sciences
NSF Science and Technology CenterSTC–88–09648
U.S.-Israeli Binational Science Foundation
National Science FoundationCCR-89-01484
Office of Naval ResearchNOO014–89–J–3042, NOO014-90-J-12S4
Center for Discrete Mathematics and Theoretical Computer Science

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