Program partitioning and synchronization on multiprocessor systems
Program partitioning and synchronization on multiprocessor systems
Automatic decomposition of scientific programs for parallel execution
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Minimum Distance: A Method for Partitioning Recurrences for Multiprocessors
IEEE Transactions on Computers
Loop distribution with arbitrary control flow
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
Maximizing parallelism and minimizing synchronization with affine transforms
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Loop parallelization algorithms: from parallelism extraction to code generation
Parallel Computing - Special issues on languages and compilers for parallel computers
Generation of Efficient Nested Loops from Polyhedra
International Journal of Parallel Programming - Special issue on instruction-level parallelism and parallelizing compilation, part 2
The parallel execution of DO loops
Communications of the ACM
Scheduling and Automatic Parallelization
Scheduling and Automatic Parallelization
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Loop Transformation Theory and an Algorithm to Maximize Parallelism
IEEE Transactions on Parallel and Distributed Systems
Maximizing Loop Parallelism and Improving Data Locality via Loop Fusion and Distribution
Proceedings of the 6th International Workshop on Languages and Compilers for Parallel Computing
Cycle Shrinking by Dependence Reduction
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing - Volume I
High-Level Synthesis of Nonprogrammable Hardware Accelerators
ASAP '00 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Code generation for multiple mappings
FRONTIERS '95 Proceedings of the Fifth Symposium on the Frontiers of Massively Parallel Computation (Frontiers'95)
On the Complexity of Loop Fusion
PACT '99 Proceedings of the 1999 International Conference on Parallel Architectures and Compilation Techniques
(R) Polynomial - Time Nested Loop Fusion with Full Parallelism
ICPP '96 Proceedings of the Proceedings of the 1996 International Conference on Parallel Processing - Volume 3
New Complexity Results on Array Contraction and Related Problems
Journal of VLSI Signal Processing Systems
Reducing off-chip memory access via stream-conscious tiling on multimedia applications
International Journal of Parallel Programming
Optimal loop parallelization for maximizing iteration-level parallelism
CASES '09 Proceedings of the 2009 international conference on Compilers, architecture, and synthesis for embedded systems
Sub-polyhedral scheduling using (unit-)two-variable-per-inequality polyhedra
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Loop alignment is a classical program transformation that can enable the fusion of parallel loops, thereby increasing locality and reducing the number of synchronizations. Although the problem is quite old in the one-dimensional case (i.e., no nested loops), it came back recently - with a multi-dimensional form - when trying to refine parallelization algorithms based on multi-dimensional schedules. The main result of this paper is that, unlike the problem in 1D, finding a multi-dimensional shift of statements that makes an innermost loop parallel is strongly NP-complete. Nevertheless, we identify some polynomially-solvable cases that can occur in practice and we show that the general problemcan be stated as a systemof integer linear constraints.