A Manual Comparison of Convex Hull Algorithms (Multimedia Exposition)
We have verified experimentally that there is at least one point set on which Andrew’s algorithm (based on Graham’s scan) to compute the convex hull of a set of points in the plane is significantly faster than a brute-force approach, thus supporting existing theoretical analysis with practical evidence. Specifically, we determined that executing Andrew’s algorithm on the point set P = {(1,4), (2,8), (3,10), (4,1), (5,7), (6,3), (7,9), (8,5), (9,2), (10,6)} takes 41 minutes and 18 seconds; the brute-force approach takes 3 hours, 49 minutes, and 5 seconds.
convex hull
efficiency
Theory of computation~Computational geometry
65:1-65:2
Multimedia Exposition
Maarten
Löffler
Maarten Löffler
Dept. of Information and Computing Sciences, Utrecht University, The Netherlands
Partially supported by the Netherlands Organisation for Scientific Research (NWO); 614.001.504.
10.4230/LIPIcs.SoCG.2019.65
A.M. Andrew. Another efficient algorithm for convex hulls in two dimensions. Information Processing Letters, 9(5):216-219, 1979. URL: http://dx.doi.org/10.1016/0020-0190(79)90072-3.
http://dx.doi.org/10.1016/0020-0190(79)90072-3
Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin, Germany, 3rd edition, 2008.
R.L. Graham. An efficient algorith for determining the convex hull of a finite planar set. Information Processing Letters, 1(4):132-133, 1972. URL: http://dx.doi.org/10.1016/0020-0190(72)90045-2.
http://dx.doi.org/10.1016/0020-0190(72)90045-2
Maarten Löffler
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode