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.
CITATION STYLE
Darte, A., & Huard, G. (2002). Complexity of multi-dimensional loop alignment. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2285, pp. 179–191). Springer Verlag. https://doi.org/10.1007/3-540-45841-7_14
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