A Geometric Programming Framework for Optimal Multi-Level Tiling
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
Locality and parallelism optimization for dynamic programming algorithm in bioinformatics
Proceedings of the 2006 ACM/IEEE conference on Supercomputing
Effective automatic parallelization of stencil computations
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
A practical automatic polyhedral parallelizer and locality optimizer
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Positivity, posynomials and tile size selection
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Efficient hybrid parallelisation of tiled algorithms on SMP clusters
International Journal of Computational Science and Engineering
Combined ILP and register tiling: analytical model and optimization framework
LCPC'05 Proceedings of the 18th international conference on Languages and Compilers for Parallel Computing
Adaptive parallel tiled code generation and accelerated auto-tuning
International Journal of High Performance Computing Applications
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For 2D iteration space tiling, we address the problem of determining the tile parameters that minimize the total execution time on a parallel machine. We consider uniform dependency computations tiled so that (at least) one of the tile boundaries is parallel to the domain boundaries. We determine the optimal tile size as a closed form solution. In addition, we determine the optimal number of processors and also the optimal slope of the oblique tile boundary. Our results are based on the BSP model, which assures the portability of the results. Our predictions are justified on a sequence global alignment problem specialized to similar sequences using Fickett's k-band algorithm, for which our optimal semi-oblique tiling yields an improvement of a factor of 2.5 over orthogonal tiling. Our optimal solution requires a block-cyclic distribution of tiles to processors. The best one can obtain with only block distribution (as many authors require) is three times slower. Furthermore, our best running time is within 10 percent of the "predicted theoretical peak" performance of the machine!.