Square meshes are not optimal for convex hull computation

• Published in: IEEE transactions on parallel and distributed systems Vol. 7; no. 6; pp. 545 - 554
• Main Authors: Bhagavathi, D., Gurla, H., Olariu, S., Schwing, J.L., Jingyuan Zhang
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.06.1996; IEEE Computer Society
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Artificial intelligence; Broadcasting; Cities and towns; Computational geometry; Computer architecture; Computer science; Computer science; control theory; systems; Exact sciences and technology; Image processing; Parallel architectures; Path planning; Pattern recognition; Pattern recognition. Digital image processing. Computational geometry; Theoretical computing; Very large scale integration; Computational geometry; Parallel algorithm; Convex hull; Image processing; Binary image; Pattern recognition; Communication
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/71.506693

Recently it has been noticed that for semigroup computations and for selection, rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts. The contribution of the paper is to provide yet another example of a fundamental problem for which this phenomenon occurs. Specifically, we show that the problem of computing the convex hull of a set of n sorted points in the plane can be solved in O(n/sup 1/8/ log /sup 3/4/) time on a rectangular mesh with multiple broadcasting of size n/sup 3/8/ log/sup 1/4/ n/spl times/n/sup 5/8//log/sup 1/4/n. The fastest previously known algorithms on a square mesh of size /spl radic/n/spl times//spl radic/n run in O(n/sup 1/6/) time in case the n points are pixels in a binary image, and in O(n/sup 1/6/log/sup 3/2/ n) time for sorted points in the plane.