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On Supernode Transformation with Minimized Total Running Time
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BibTeX
@MISC{Hodzic_onsupernode,
author = {Edin Hodzic and Weijia Shang},
title = {On Supernode Transformation with Minimized Total Running Time},
year = {}
}
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Abstract
With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses how to find 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 sufficiently 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 s...
Keyphrases
supernode transformation minimized total running time optimal supernode size closed form expression supernode size communication cost special case hyperplane direction real positive root multiple supernodes dimensional algorithm problem startup penalty total execution time optimal supernode relative side length single processor order polynomial distributed memory parallel computer uniform dependency large supernodes relative side length parallel program n-dimensional algorithm problem optimal supernode
