On the parallel-decomposability of geometric problems |
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Authors: | Mikhail J Atallah and Jyh -Jong Tsay |
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Affiliation: | (1) Department of Computer Science, Purdue University, 47907 West Lafayette, IN, USA;(2) Institute of Computer Science and Information Engineering, National Chung Chen University, 62107 Chiayi, Taiwan, Republic of China |
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Abstract: | There is a large and growing body of literature concerning the solutions of geometric problems on mesh-connected arrays of processors. Most of these algorithms are optimal (i.e., run in timeO(n
1/d
) on ad-dimensionaln-processor array), and they all assume that the parallel machine is trying to solve a problem of sizen on ann-processor array. Here we investigate the situation where we have a mesh of sizep and we are interested in using it to solve a problem of sizen >p. The goal we seek is to achieve, when solving a problem of sizen >p, the same speed up as when solving a problem of sizep. We show that for many geometric problems, the same speedup can be achieved when solving a problem of sizen >p as when solving a problem of sizep.The research of M. J. Atallah was supported by the Office of Naval Research under Contracts N00014-84-K-0502 and N00014-86-K-0689, the Air Force Office of Scientific Research under Grant AFOSR-90-0107, the National Science Foundation under Grant DCR-8451393, and the National Library of Medicine under Grant R01-LM05118. Jyh-Jong Tsay's research was partially supported by the Office of Naval Research under Contract N00014-84-K-0502, the Air Force Office of Scientific Research under Grant AFOSR-90-0107, and the National Science Foundation under Grant DCR-8451393. |
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Keywords: | Computational geometry Mesh-connected arrays of processors Parallel algorithms |
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