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DOI: 10.4230/LIPIcs.SoCG.2016.48

Congruence Testing of Point Sets in 4-Space

Authors: Heuna Kim and Günter Rote

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

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.

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Heuna Kim and Günter Rote. Congruence Testing of Point Sets in 4-Space. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{kim_et_al:LIPIcs.SoCG.2016.48,
  author =	{Kim, Heuna and Rote, G\"{u}nter},
  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 =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.48},
  URN =		{urn:nbn:de:0030-drops-59409},
  doi =		{10.4230/LIPIcs.SoCG.2016.48},
  annote =	{Keywords: Congruence Testing Algorithm, Symmetry, Computational Geometry}
}

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Congruence Testing of Point Sets in 4-Space

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