TY - GEN

T1 - NC1 parallel 3D convex hull algorithm

AU - Amato, Nancy M.

AU - Preparata, Franco P.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - In this paper we present an O(log n) time parallel algorithm for computing the convex hull of n points in R3. This algorithm uses O(n1+α) processors on a CREW PRAM, for any constant 0 < α ≤ 1. So far, all adequately documented parallel algorithms proposed for this problem use time at least O(log2 n). In addition, the algorithm presented here is the first parallel algorithm for the three-dimensional convex hull problem that is not based on the serial divide-and-conquer algorithm of Preparata and Hong, whose crucial operation is the merging of the convex hulls of two linearly separated points sets. The contributions of this paper are therefore (i) an O(log n) time parallel algorithm for the three-dimensional convex hull problem, and (ii) a parallel algorithm for this problem that does not follow the traditional divide-and-conquer paradigm.

AB - In this paper we present an O(log n) time parallel algorithm for computing the convex hull of n points in R3. This algorithm uses O(n1+α) processors on a CREW PRAM, for any constant 0 < α ≤ 1. So far, all adequately documented parallel algorithms proposed for this problem use time at least O(log2 n). In addition, the algorithm presented here is the first parallel algorithm for the three-dimensional convex hull problem that is not based on the serial divide-and-conquer algorithm of Preparata and Hong, whose crucial operation is the merging of the convex hulls of two linearly separated points sets. The contributions of this paper are therefore (i) an O(log n) time parallel algorithm for the three-dimensional convex hull problem, and (ii) a parallel algorithm for this problem that does not follow the traditional divide-and-conquer paradigm.

UR - http://www.scopus.com/inward/record.url?scp=0027837127&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027837127&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027837127

SN - 0897915828

T3 - Proceedings of the 9th Annual Symposium on Computational Geometry

SP - 289

EP - 297

BT - Proceedings of the 9th Annual Symposium on Computational Geometry

A2 - Anon, null

PB - Publ by ACM

T2 - Proceedings of the 9th Annual Symposium on Computational Geometry

Y2 - 19 May 1993 through 21 May 1993

ER -