On supernode transformation with minimized total running time

Hodzic, E.; Shang, Weijia

doi:10.1109/asap.1996.544416

Cited by 2 publications

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On supernode transformation with minimized total running time

Hodzic

Shang

1998

IEEE Trans. Parallel Distrib. Syst.

Self Cite

View full text Add to dashboard Cite

With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses how to nd an optimal supernode size and optimal supernode relative side lengths of a supernode transformation (also known as tiling). We identify three parameters of supernode transformation: supernode size, relative side lengths, and cutting hyperplane directions. For algorithms with perfectly nested loops and uniform dependencies, for su ciently large supernodes and number of processors, and for the case where multiple supernodes are mapped to a single processor, we give an order n polynomial whose real positive roots include the optimal supernode size. For two special cases: (1) two dimensional algorithm problems and (2) n-dimensional algorithm problems where the communication cost is dominated by the startup penalty and therefore, can be approximated by a constant, we give a closed form expression for the optimal supernode size, which is independent of the supernode relative side lengths and cutting hyperplanes. For the case where the algorithm iteration index space and the supernodes are hyperrectangular, we give closed form expressions for the optimal supernode relative side lengths. Our experiment shows a good match of the closed form expressions with experimental data.

show abstract