Parallel Algorithms and Applications

PLANAR CONVEX HULL ALGORITHMS ON LINEAR ARRAYS

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DOI:: 10.1080/10637199608915606

DORIS L. CARVER^a, JIGANG LIU^a & S. Q. ZHENG^a

pages 59-70

Available online: 30 Mar 2007

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Abstract

This paper presents two planar convex hull algorithms on linear array. The First algorithm is for the case such that n ≤ p, where n and p are the number of points in S and the number of processors, respectively. The algorithm runs in O(n) which is optimal. The second algorithm is designed for a general case such that n > p. The algorithm runs in O((n/p) log(n/p)) time, which is also optimal. Both algorithms have been extended to d-dimensional mesh-connected array with O(d²n^1/d ) in time for the case such as n < p, and O((n/p)log(n/p) + np^1/d−1) in time for the case such as n >> p and p ^1/ >> 2, which are both optimal.