Improvements on bottleneck matching and related problems using geometry

Alon Efrat, Alon Itai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

33 Citations (Scopus)

Abstract

Let A and B be two sets of n objects in Rd. We propose to use bottleneck matching as a convenient way for measuring the resemblance between them, and present several algorithms for computing, as well as approximating, this resemblance. The running time of all these algorithms is close to O(n1.5). For instance, if the objects are points in the plane, the running time is O(n1.5 log n). We also consider the problem of finding a translation of B that maximizes the resemblance to A under the bottleneck matching criterion. When A and B are point-sets in the plane, we present an O(n5 log n) time algorithm for determining whether for some translated copy the resemblance gets below a given ρ, improving the previous result of Alt, Mehlhorn, Wagener and Welzl by a factor of almost n. We use this result to compute the smallest such ρ in time O(n5 log2 n), and give an efficient approximation scheme for this problem.

Original languageEnglish (US)
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherACM
Pages301-310
Number of pages10
StatePublished - 1996
Externally publishedYes
EventProceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA
Duration: May 24 1996May 26 1996

Other

OtherProceedings of the 1996 12th Annual Symposium on Computational Geometry
CityPhiladelphia, PA, USA
Period5/24/965/26/96

Fingerprint

Geometry
Approximation Scheme
Point Sets
Maximise
Computing
Object

ASJC Scopus subject areas

  • Chemical Health and Safety
  • Software
  • Safety, Risk, Reliability and Quality
  • Geometry and Topology

Cite this

Efrat, A., & Itai, A. (1996). Improvements on bottleneck matching and related problems using geometry. In Proceedings of the Annual Symposium on Computational Geometry (pp. 301-310). ACM.

Improvements on bottleneck matching and related problems using geometry. / Efrat, Alon; Itai, Alon.

Proceedings of the Annual Symposium on Computational Geometry. ACM, 1996. p. 301-310.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Efrat, A & Itai, A 1996, Improvements on bottleneck matching and related problems using geometry. in Proceedings of the Annual Symposium on Computational Geometry. ACM, pp. 301-310, Proceedings of the 1996 12th Annual Symposium on Computational Geometry, Philadelphia, PA, USA, 5/24/96.
Efrat A, Itai A. Improvements on bottleneck matching and related problems using geometry. In Proceedings of the Annual Symposium on Computational Geometry. ACM. 1996. p. 301-310
Efrat, Alon ; Itai, Alon. / Improvements on bottleneck matching and related problems using geometry. Proceedings of the Annual Symposium on Computational Geometry. ACM, 1996. pp. 301-310
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