Geometric pattern matching in d-dimensional space

L. Paul Chew, Dorit Dor, Alon Efrat, Klara Kedem

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

10 Scopus citations

Abstract

We show that, using the L metric, the minimum Hausdorff distance under translation between two point sets of cardinality n in ddimensional space can be computed in time O(n(4d-2)/31og2 n) for d > 3. Thus we improve the previous time bound of O(n2d-2 log2 n) due to Chew and Kedem. For d = 3 we obtain a better result of O(n3 log2 n) time by exploiting the fact that the union of n axis-parallel unit cubes can be decomposed into O(n) disjoint axls-parallel boxes. We prove that the number of different translations that azhieve the minimum Hausdorff distance in dspace is Θ (n[3d/2]). Furthermore, we present an algorithm which computes the minimum Hausdorff distance under the L2 metric in d-space in time O(n[3d/2]+l log3 n).

Original languageEnglish
Title of host publicationAlgorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings
EditorsPaul Spirakis
PublisherSpringer Verlag
Pages264-279
Number of pages16
ISBN (Print)3540603131, 9783540603139
StatePublished - 1 Jan 1995
Event3rd Annual European Symposium on Algorithms, ESA 1995 - Corfu, Greece
Duration: 25 Sep 199527 Sep 1995

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume979
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd Annual European Symposium on Algorithms, ESA 1995
Country/TerritoryGreece
CityCorfu
Period25/09/9527/09/95

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