Improvements on geometric pattern matching problems

L. Paul Chew, Klara Kedem

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

33 Scopus citations


We consider the following geometric pattern matching problem: find the minimum Hausdorff distance between two point sets under translation with L1 or L as the underlying metric. Huttenlocher, Kedem, and Sharir have shown that this minimum distance can be found by constructing the upper envelope of certain Voronoi surfaces. Further, they show that if the two sets are each of cardinality n then the complexity of the upper envelope of such surfaces is Ω(n3). We examine the question of whether one can get around this cubic lower bound, and show that under the L1 and L metrics, the time to compute the minimum Hausdorff distance between two point sets is On2 log2n).

Original languageEnglish
Title of host publicationAlgorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings
EditorsOtto Nurmi, Esko Ukkonen
PublisherSpringer Verlag
Number of pages8
ISBN (Print)9783540557067
StatePublished - 1 Jan 1992
Externally publishedYes
Event3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992 - Helsinki, Finland
Duration: 8 Jul 199210 Jul 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume621 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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