Theory of linear and integer programming
Theory of linear and integer programming
Automatic translation of FORTRAN programs to vector form
ACM Transactions on Programming Languages and Systems (TOPLAS)
A global approach to detection of parallelism
A global approach to detection of parallelism
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Supercompilers for parallel and vector computers
Supercompilers for parallel and vector computers
Selected papers of the second workshop on Languages and compilers for parallel computing
Semantical interprocedural parallelization: an overview of the PIPS project
ICS '91 Proceedings of the 5th international conference on Supercomputing
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
Mapping uniform loop nests onto distributed memory architectures
Parallel Computing
Automating non-unimodular loop transformations for massive parallelism
Parallel Computing
Integration, the VLSI Journal
PPOPP '95 Proceedings of the fifth ACM SIGPLAN symposium on Principles and practice of parallel programming
Affine-by-statement scheduling of uniform and affine loop nests over parametric domains
Journal of Parallel and Distributed Computing
Maximizing parallelism and minimizing synchronization with affine transforms
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
The parallel execution of DO loops
Communications of the ACM
Optimizing Supercompilers for Supercomputers
Optimizing Supercompilers for Supercomputers
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
A Loop Transformation Theory and an Algorithm to Maximize Parallelism
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
Optimal Fine and Medium Grain Parallelism Detection in Polyhedral Reduced Dependence Graphs
PACT '96 Proceedings of the 1996 Conference on Parallel Architectures and Compilation Techniques
Automatic Blocking of Nested Loops
Automatic Blocking of Nested Loops
Optimizing supercompilers for supercomputers
Optimizing supercompilers for supercomputers
Automatic speculative parallelization of loops using polyhedral dependence analysis
Proceedings of the First International Workshop on Code OptimiSation for MultI and many Cores
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This chapter is devoted to a comparative survey of loop parallelization algorithms. Various algorithms have been presented in the literature, such as those introduced by Allen and Kennedy,Wolf and Lam, Darte and Vivien, and Feautrier. These algorithms make use of different mathematical tools. Also, they do not rely on the same representation of data dependences. In this chapter, we survey each of these algorithms, and we assess their power and limitations, both through examples and by stating "optimality" results. An important contribution of this chapter is to characterize which algorithm is the most suitable for a given representation of dependences. This result is of practical interest, as it provides guidance for a compiler-parallelizer: given the dependence analysis that is available, the simplest and cheapest parallelization algorithm that remains optimal should be selected.