Congruence Testing of Point Sets in 4-Space

Authors Heuna Kim, Günter Rote

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Heuna Kim
Günter Rote

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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)


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.
  • Congruence Testing Algorithm
  • Symmetry
  • Computational Geometry


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