Enumerative combinatorics
Systematic design approaches for algorithmically specified systolic arrays
Computer architecture
Journal of Parallel and Distributed Computing
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
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Using a directed acyclic graph (dag) model of algorithms, we solve a problem related to precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parametrized by n, compute a lower bound on the number of processors required by the schedule as a function of n. In our formulation, the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions dn to a set of parametric linear Diophantine equations. We illustrate an algorithm based on generating functions for constructing a formula for these numbers dn. The algorithm has been implemented as a Mathematica program. An example run and the symbolic formula for processor lower bounds automatically produced by the algorithm for Gaussian Elimination is presented.