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  • Abstract - An Approach to Checking Link Conflicts in the Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays
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An Approach to Checking Link Conflicts in the Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays
July 1999 (vol. 48 no. 7)
pp. 732-737

Abstract—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 $O(N^{2n})$ or $O(N^{n-1})$, 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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Index Terms:
Uniform dependence algorithms, lower dimensional arrays, space-time mapping, link conflict, mixed integer linear programming, Hermite normal form, Smith normal form.
Citation:
Jenn-Yang Ke, Jong-Chuang Tsay, "An Approach to Checking Link Conflicts in the Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays," IEEE Transactions on Computers, vol. 48, no. 7, pp. 732-737, July 1999, doi:10.1109/12.780880
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