Square meshes are not optimal for convex hull computation
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 occ...
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Published in | IEEE transactions on parallel and distributed systems Vol. 7; no. 6; pp. 545 - 554 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Los Alamitos, CA
IEEE
01.06.1996
IEEE Computer Society |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 1045-9219 1558-2183 |
DOI: | 10.1109/71.506693 |