Expander-based-approach to geometric optimization

Matthew J. Katz, Micha Sharir

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

20 Scopus citations

Abstract

We present a new approach to problems in geometric optimization that are traditionally solved using the parametric searching technique of Megiddo. Our new approach is based on expander graphs and is conceptually much simpler and has more explicit geometric flavor. It does not require parallelization or randomization, and it exploits recent range-searching techniques of Matousek and others. We exemplify the technique on three problems, the slope selection problem, the planar distance selection problem, and the planar two-center problem. For the first problem we develop an O(n log3 n) solution, which, although suboptimal, is very simple. The second and third problems are more typical examples of our approach. Our solutions have, respectively, running time O(n4/3 log3+δ n), for any δ > 0, and O(n2 log3 n), comparable with the respective solutions of [2, 5].

Original languageEnglish
Title of host publicationProceedings of the 9th Annual Symposium on Computational Geometry
PublisherPubl by ACM
Pages198-207
Number of pages10
ISBN (Print)0897915828, 9780897915823
DOIs
StatePublished - 1 Jan 1993
Externally publishedYes
EventProceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA
Duration: 19 May 199321 May 1993

Publication series

NameProceedings of the 9th Annual Symposium on Computational Geometry

Conference

ConferenceProceedings of the 9th Annual Symposium on Computational Geometry
CitySan Diego, CA, USA
Period19/05/9321/05/93

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