Partitioning and Mapping Algorithms into Fixed Size Systolic Arrays
IEEE Transactions on Computers
Regular interactive algorithms and their implementations on processor arrays
Regular interactive algorithms and their implementations on processor arrays
Theory of linear and integer programming
Theory of linear and integer programming
VLSI array processors
Synthesizing Linear Array Algorithms from Nested FOR Loop Algorithms
IEEE Transactions on Computers
Time Optimal Linear Schedules for Algorithms with Uniform Dependencies
IEEE Transactions on Computers
Closed-form mapping conditions for the synthesis of linear processor arrays
Journal of VLSI Signal Processing Systems
Optimal Synthesis of Algorithm-Specific Lower-Dimensional Processor Arrays
IEEE Transactions on Parallel and Distributed Systems
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
The parallel execution of DO loops
Communications of the ACM
Mapping Nested Loop Algorithms into Multidimensional Systolic Arrays
IEEE Transactions on Parallel and Distributed Systems
On Time Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays
IEEE Transactions on Parallel and Distributed Systems
Proceedings of the 1994 International Conference on Parallel and Distributed Systems
Automatic synthesis of systolic arrays from uniform recurrent equations
ISCA '84 Proceedings of the 11th annual international symposium on Computer architecture
| Hi-index | 14.98 |
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.