On optimal size and shape of supernode transformations

Hodzic, E.; Shang, Weijia

doi:10.1109/icpp.1996.538556

Cited by 3 publications

(2 citation statements)

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“…To present our analysis, the following additional notation is used (it was first introduced in [13]). The column vector l ¼ ½l 1 ; :::; l n T is called supernode side length vector.…”

Section: Matrix H Factorizationmentioning

confidence: 99%

“…Parameters of the supernode transformation may be used to tune the balance between computation and communication in order to minimize the total execution time of a parallel program. Supernode transformation was proposed in [17] and has been studied in [1], [4], [3], [2], [5], [15], [9], [13], [14], [12], [10], [11], [16], [19], [20], [22], [27], [29], [28], etc., to reduce communication overhead, synchronization overhead, or memory hierarchy inefficiency.…”

Section: Introductionmentioning

confidence: 99%

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On time optimal supernode shape

Hodzic

Shang

2002

IEEE Trans. Parallel Distrib. Syst.

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With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses the selection of an optimal supernode shape of a supernode transformation (also known as tiling). We identify three parameters of a supernode transformation: supernode size, relative side lengths, and cutting hyperplane directions. For supernode transformations on algorithms with perfectly nested loops and uniform dependencies, we prove the optimality of a constant linear schedule vector and give a necessary and sufficient condition for optimal relative side lengths. We also prove that the total running time is minimized by a cutting hyperplane direction matrix from a particular subset of all valid directions and we discuss the cases where this subset is unique. The results are derived in continuous space and should be considered approximate. Our model does not include cache effects and assumes an unbounded number of available processors, the communication cost approximated by a constant, uniform dependences, and loop bounds known at compile time. A comprehensive example is discussed with an application of the results to the Jacobi algorithm.

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“…To present our analysis, the following additional notation is used (it was first introduced in [13]). The column vector l ¼ ½l 1 ; :::; l n T is called supernode side length vector.…”

Section: Matrix H Factorizationmentioning

confidence: 99%