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DOI: 10.4230/LIPIcs.SoCG.2016.48
URN: urn:nbn:de:0030-drops-59409
URL: http://drops.dagstuhl.de/opus/volltexte/2016/5940/
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Kim, Heuna ; Rote, GŁnter

Congruence Testing of Point Sets in 4-Space

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LIPIcs-SoCG-2016-48.pdf (0.5 MB)


Abstract

We give a deterministic O(n log n)-time algorithm to decide if two n-point sets in 4-dimensional Euclidean space are the same up to rotations and translations. It has been conjectured that O(n log n) algorithms should exist for any fixed dimension. The best algorithms in d-space so far are a deterministic algorithm by Brass and Knauer [Int. J. Comput. Geom. Appl., 2000] and a randomized Monte Carlo algorithm by Akutsu [Comp. Geom., 1998]. They take time O(n^2 log n) and O(n^(3/2) log n) respectively in 4-space. Our algorithm exploits many geometric structures and properties of 4-dimensional space.

BibTeX - Entry

@InProceedings{kim_et_al:LIPIcs:2016:5940,
  author =	{Heuna Kim and G{\"u}nter Rote},
  title =	{{Congruence Testing of Point Sets in 4-Space}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5940},
  URN =		{urn:nbn:de:0030-drops-59409},
  doi =		{10.4230/LIPIcs.SoCG.2016.48},
  annote =	{Keywords: Congruence Testing Algorithm, Symmetry, Computational Geometry}
}

Keywords: Congruence Testing Algorithm, Symmetry, Computational Geometry
Seminar: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 09.06.2016


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