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Scalable 2d convex hull and triangulation algorithms for coarse grained multicomputers

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3 Author(s)
A. Ferreira ; LIP-ENS Lyon, France ; A. Rau-Chaplin ; S. Ueda

In this paper we describe scalable parallel algorithms for building the Convex Hull and a Triangulation of a given point set in R 2. These algorithms are designed for the coarse grained multicomputer model: p processors with O(n/p)≫O(1) local memory each, connected to some arbitrary interconnection network (e.g. mesh, hypercube, omega). They require time O(Tsequential/p+Ts (n, p)), where Ts(n, p) refers to the time of a global sort of n data on a p processor machine. Furthermore, they involve only a constant number of global communication rounds. Since computing either 2d Convex Hull or Triangulation requires time Tsequential=Θ(n log n n) these algorithms either ran in optimal time, Θ(n log n/p), or in sort time, Ts(n, p), for the interconnection network in question. These results become optimal when Tsequential/p dominates Ts (n, p), for instance when randomized sorting algorithms are used, or for interconnection networks like the mesh for which optimal sorting algorithms exist

Published in:

Parallel and Distributed Processing, 1995. Proceedings. Seventh IEEE Symposium on

Date of Conference:

25-28 Oct 1995