Abstract
Given a finite set of points P in ℝd, the diameter of P is defined as the maximum distance between two points of P. We propose a very simple algorithm to compute the diameter of a finite set of points. Although the algorithm is not worst-case optimal, it appears to be extremely fast for a large variety of point distributions.
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N. M. Amato, M. T. Goodrich, and E. A. Ramos. Parallel algorithms for higher-dimensional convex hulls. In Proc. 35th Annu. IEEE Sympos. Found. Comput. Sci., pages 683–694, 1994.
S. Bespamyatnikh. An efficient algorithm for the three-dimensional diameter problem. In Proc. 9th Annu. ACM-SIAM Symp. Discrete Algorithms, pages 137–146, 1998.
K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry. Discrete Comput. Geom., 4:387–421, 1989.
S. Har-Peled. A practical approach for computing the diameter of a pointset. In Symposium on Computational Geometry (SOCG’2001), pages 177–186, 2001.
Grégoire Malandain and Jean-Daniel Boissonnat. Computing the diameter of a point set. Research report RR-4233, INRIA, Sophia-Antipolis, July 2001. http://www.inria.fr/rrrt/rr-4233.html.
F.P. Preparata and M.I. Shamos. Computational Geometry: An Introduction. Springer Verlag, October 1990. 3rd edition.
E. Ramos. Construction of 1-d lower envelopes and applications. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 57–66, 1997.
E. Ramos. Intersection of unit-balls and diameter of a point set in R 3. Comput. Geom. Theory Application, 8:57–65, 1997.
Edgar A. Ramos. Deterministic algorithms for 3-D diameter and some 2-D lower envelopes. In Proc. 16th Annu. ACM Sympos. Comput. Geom., pages 290–299, 2000.
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Malandain, G., Boissonnat, JD. (2002). Computing the Diameter of a Point Set. In: Braquelaire, A., Lachaud, JO., Vialard, A. (eds) Discrete Geometry for Computer Imagery. DGCI 2002. Lecture Notes in Computer Science, vol 2301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45986-3_18
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DOI: https://doi.org/10.1007/3-540-45986-3_18
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