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An approach to checking link conflicts in the mapping of uniform dependence algorithms into lower dimensional processor arrays

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2 Author(s)
Jenn-Yang Ke ; Dept. of Appl. Math., Tatung Inst. of Technol., Taipei, Taiwan ; Jong-Chuang Tsay

In this paper, we propose an enumeration method to check link conflicts in the mapping of n-dimensional uniform dependence algorithms with arbitrary convex index sets into k-dimensional processor arrays. Previous methods on checking the link conflicts had to examine either the whole index set or the I/O spaces whose size are O(N2n) or O(Nn-1), respectively, where N is the problem size of the n-dimensional uniform dependence algorithm. In our approach, checking the link conflicts is done by enumerating integer solutions of a mixed integer linear program. In order to enumerate integer solutions efficiently, a representation of the integer solutions is devised so that the size of the space enumerated is O((2N)n-k). Thus, our approach to checking link conflicts has better performance than previous methods, especially for larger k. For the special case k=n-2, we show that link conflicts can be checked by solving two linear programs in one variable

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Computers, IEEE Transactions on  (Volume:48 ,  Issue: 7 )