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.
@InProceedings{loffler:LIPIcs.SoCG.2019.65, author = {L\"{o}ffler, Maarten}, title = {{A Manual Comparison of Convex Hull Algorithms}}, booktitle = {35th International Symposium on Computational Geometry (SoCG 2019)}, pages = {65:1--65:2}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-104-7}, ISSN = {1868-8969}, year = {2019}, volume = {129}, editor = {Barequet, Gill and Wang, Yusu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.65}, URN = {urn:nbn:de:0030-drops-104690}, doi = {10.4230/LIPIcs.SoCG.2019.65}, annote = {Keywords: convex hull, efficiency} }
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