1988 Fiscal Year Final Research Report Summary
Parallel Algorithms on Mesh-Connected Processor Arrays and Their Time Efficiencies
| Project/Area Number |
62580016
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Informatics
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| Research Institution | Gunma University |
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Principal Investigator |
SADO Kazuhiro Faculty of Engineering, Gunma University, 工学部, 助教授 (10162512)
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| Co-Investigator(Kenkyū-buntansha) |
IGARASHI Yoshihide Faculty of Engineering, Gunma University, 工学部, 教授 (60006260)
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| Project Period (FY) |
1987 – 1988
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| Keywords | parallel algorithm / sorting / mesh-connected processor array / SIMD / 時間計算量 |
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| Research Abstract |
We designed three sorting algorithms and a number of their variations on the mesh-connected model. These three algorithms are called the shear sort, the pseudo-merge sort and the predistributed column merge sort. The computing times of these algorithms are n log_2n, 6.5n and 5.5n steps within their leading terms, respectively for sorting n^2 items. although our algorithms are asymptotically inferior to the 3n-time algorithms, for practical values of n our algorithms are much faster than their algorithms. Furthermore, the control structures of our algorithms are particularly simple, and therefore they are suitable to be realized on a VLSI chip.
Our algorithms are some combinations of the parallel bubble sorts in differenct directions. We studied the property of the parallel bubbling system. We introduced a function called POTENTIAL witch exactly evaluates the number of steps needed to route all items to their final positions by the parallel bubbling. Using this function we can accurately analyze the time efficienceis of our algorithms. This function is also useful to the correctness proofs of the algorithms.
The mesh-connected model can be naturally generalized to multi-dimensional mesh-connected models. For each d<greater than or equal>, we designed a (2d-1)n+O(n^<(d-2)/(d-1)>) time algorithm for sorting n^d items on a d-dimensional mesh-connected model. We also developed a general technique called the chain argument to derive time lower bounds for various indexing functions. We showed that any algorithms for sorting n^2 items on the mesh-connected model takes at least 2.27n steps no matter what indexing function is used.
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Research Products
(6 results)
