Exact Point Pattern Matching and the Number of Congruent Triangles in a Three-Dimensional Pointset

Authors:
Peter Brass
Affiliations:
-
Venue:
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Year:
2000

Citing 13
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Abstract

In this paper we study the complexity of the problem of finding all subsets of an n-point set B in threedimensional euclidean space that are congruent to a given m-point set A. We obtain a randomized O(mn7/4 log nβ(n))-algorithm for this problem, improving on previous O(mn5/2) and O(mn2)-algorithms of Boxer. By the same method we prove an O(n7/4 β(n)) upper bound on the number of triangles congruent to a given one among n points in threedimensional space, improving an O(n9/5)-bound of Akutsu et al. The corresponding lower bound for both problems is Ω(n4/3).