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• W2019403731 abstract "This paper describes several parallel algorithms that solve geometric problems. The algorithms are based on a vector model of computation-the scan model . The purpose of this paper is both to show how the model can be used and to formulate a set of practical algorithms. The scan model is based on a small set of operations on vectors of atomic values. It differs from the P-RAM models both in that it includes a set of scan primitives, also called parallel prefix computations, and in that it is a strictly data-parallel model. A very useful abstraction in the scan model is the segment abstraction, the subdivision of a vector into a collection of independent smaller vectors. The segment abstraction permits a clean formulation of divide-and-conquer algorithms and is used heavily in the algorithms described in this paper. Within the scan model, using the operations and routines defined, the paper describes a k -D tree algorithm requiring O (lg n ) calls to the primitives for n points, a closest-pair algorithm requiring O (lg n ) calls to the primitives, a line-drawing algorithm requiring O (1) calls to the primitives, a line-of-sight algorithm requiring O (1) calls to the primitives, and finally, three different convex-hull algorithms. The last convex-hull algorithm, merge-hull, utilizes a generalized binary search technique using divide-and-conquer with the segment abstraction. The paper also describes how to implement the CREW version of Cole's merge sort in O (lg n ) calls to the primitives. All these algorithms should be noted for their simplicity rather than their complexity; many of them are parallel versions of known serial algorithms. Most of the algorithms discussed in this paper have been implemented on the Connection Machine, a highly parallel single instruction multiple data computer." @default.
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• W2019403731 date "1994-02-01" @default.
• W2019403731 modified "2023-10-16" @default.
• W2019403731 title "Parallel solutions to geometric problems in the scan model of computation" @default.
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• W2019403731 doi "https://doi.org/10.1016/s0022-0000(05)80023-6" @default.
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