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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
ASCII Text
x 
 
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.
 
 
BibTex
x
 
@article{ 10.1109/12.780880,
author = {Jenn-Yang Ke and Jong-Chuang Tsay},
title = {An Approach to Checking Link Conflicts in the Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays},
journal ={IEEE Transactions on Computers},
volume = {48},
number = {7},
issn = {0018-9340},
year = {1999},
pages = {732-737},
doi = {http://doi.ieeecomputersociety.org/10.1109/12.780880},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - An Approach to Checking Link Conflicts in the Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays
IS - 7
SN - 0018-9340
SP732
EP737
EPD - 732-737
A1 - Jenn-Yang Ke,
A1 - Jong-Chuang Tsay,
PY - 1999
KW - Uniform dependence algorithms
KW - lower dimensional arrays
KW - space-time mapping
KW - link conflict
KW - mixed integer linear programming
KW - Hermite normal form
KW - Smith normal form.
VL - 48
JA - IEEE Transactions on Computers
ER -
 

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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