On synthesizing systolic arrays from recurrence equations with linear dependencies
Proc. of the sixth conference on Foundations of software technology and theoretical computer science
Enumerative combinatorics
Optimal Systolic Design for the Transitive Closure and the Shortest Path Problems
IEEE Transactions on Computers
Systematic design approaches for algorithmically specified systolic arrays
Computer architecture
Journal of Parallel and Distributed Computing
A Note on the Linear Transformation Method for Systolic Array Design
IEEE Transactions on Computers
A new systolic architecture for the algebraic path problem
Systolic array processors
An optimal solution for Gauss-Jordan elimination of 2D systolic arrays
Systolic array processors
A spacetime-minimal systolic array for matrix product
Systolic array processors
Time Optimal Linear Schedules for Algorithms with Uniform Dependencies
IEEE Transactions on Computers
The ALPHA language and its use for the design of systolic arrays
Journal of VLSI Signal Processing Systems - Special issue: algorithms and parallel VSLI architecture
Journal of Combinatorial Theory Series A
Mapping fundamental algorithms onto multiprocessor architectures
Mapping fundamental algorithms onto multiprocessor architectures
Parametric Analysis of Polyhedral Iteration Spaces
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Journal of the ACM (JACM)
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
The parallel execution of DO loops
Communications of the ACM
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A Processor-Time-Minimal Systolic Array for Cubical Mesh Algorithms
IEEE Transactions on Parallel and Distributed Systems
A Processor-Time-Minimal Systolic Array for Transitive Closure
IEEE Transactions on Parallel and Distributed Systems
A Period-Processor-Time-Minimal Schedule for Cubical Mesh Algorithms
IEEE Transactions on Parallel and Distributed Systems
Space-Optimal Linear Processor Allocation for Systolic Arrays Synthesis
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
A Processor-Time-Minimal Schedule for 3D Rectilinear Mesh Algorithms
ASAP '95 Proceedings of the IEEE International Conference on Application Specific Array Processors
Automatic synthesis of systolic arrays from uniform recurrent equations
ISCA '84 Proceedings of the 11th annual international symposium on Computer architecture
Computational Aspects of VLSI
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We consider computations suitable for systolic arrays, often called regular array computations or systems of uniform recurrence relations. In such computations, the tasks to be computed are viewed as the nodes of a directed acyclic graph (dag), where the data dependencies are represented as arcs. A processor-time-minimal schedule measures the minimum number of processors needed to extract the maximum parallelism from the dag. We present a technique for finding a lower bound on the number of processors needed to achieve a given schedule of an algorithm represented as a dag. The application of this technique is illustrated with a tensor product computation. We then consider the free schedule of algorithms for matrix product, Gaussian elimination, and transitive closure. For each problem, we provide a time-minimal processor schedule that meets the computed processor lower bounds, including the one for tensor product.