Geometric pattern matching in d-dimensional space

  • L. Paul Chew
  • Dorit Dor
  • Alon Efrat
  • Klara Kedem
Session 4. Chair: Marek Karpinski

DOI: 10.1007/3-540-60313-1_149

Part of the Lecture Notes in Computer Science book series (LNCS, volume 979)
Cite this paper as:
Paul Chew L., Dor D., Efrat A., Kedem K. (1995) Geometric pattern matching in d-dimensional space. In: Spirakis P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg

Abstract

We show that, using the L metric, the minimum Hausdorff distance under translation between two point sets of cardinality n in d-dimensional space can be computed in time O(n(4d−2)/3 log2n) for d>3. Thus we improve the previous time bound of O(n2d−2 log2n) due to Chew and Kedem. For d=3 we obtain a better result of O(n3 log2n) time by exploiting the fact that the union of n axis-parallel unit cubes can be decomposed into O(n) disjoint axis-parallel boxes. We prove that the number of different translations that achieve the minimum Hausdorff distance in d-space 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⌋+1 log3n).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • L. Paul Chew
    • 1
  • Dorit Dor
    • 2
  • Alon Efrat
    • 2
  • Klara Kedem
    • 3
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.Department of Math and CSBen Gurion UniversityBeer-ShevaIsrael

Personalised recommendations