VLSI array processors
Data optimization: allocation of arrays to reduce communication on SIMD machines
Journal of Parallel and Distributed Computing - Massively parallel computation
Time Optimal Linear Schedules for Algorithms with Uniform Dependencies
IEEE Transactions on Computers
The data alignment phase in compiling programs for distributed-memory machines
Journal of Parallel and Distributed Computing
Mobile and replicated alignment of arrays in data-parallel programs
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Concrete Math
Constructive Methods for Scheduling Uniform Loop Nests
IEEE Transactions on Parallel and Distributed Systems
Loop Transformation Using Nonunimodular Matrices
IEEE Transactions on Parallel and Distributed Systems
Code Generation in Automatic Parallelizers
Proceedings of the IFIP WG10.3 Working Conference on Applications in Parallel and Distributed Computing
A characterization of one-to-one modular mappings
SPDP '95 Proceedings of the 7th IEEE Symposium on Parallel and Distributeed Processing
Systematic optimization of basic linear algebra computations for distributed-memory systems
Systematic optimization of basic linear algebra computations for distributed-memory systems
Generation of Injective and Reversible Modular Mappings
IEEE Transactions on Parallel and Distributed Systems
Programming and Computing Software
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Time-space transformations and data alignments that can lead to efficient execution of parallel programs have been extensivelystudied. Recently, modular time-space transformations have been proposed to generate a class of algorithm mappings that cannot be described by linear time-space transformations. This paper proposes a new class of data alignments, called expanded modular data alignments (EMDAs), for programs that result from modular time-space transformations. An EMDA subsumes multiple modular data alignments, whichare described by affine functions modulo a constant vector. Conditions of a modular time-space mapping and an EMDA for perfect alignment are described. However, these conditions together with other conditions for validity and optimality of a modular mapping introduce nonlinear constraints in the problem of generating modular mappings. A method of O(n^2) complexity is provided to choose some entries of a transformation matrix so that nonlinear constraints are transformed into linear ones, where n is the dimensionof the computation domain (e.g., the number of nested loops). Although the solution space of the problem is reduced by assigning fixed values to some entries, the proposed heuristic attempts to minimize the number of the fixed entries and consequently to exclude as few solutions as possible.