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Parallelization of divide-and-conquer by translation to nested loops

Published online by Cambridge University Press:  01 May 1999

CHRISTOPH A. HERRMANN
Affiliation:
Fakultät für Mathematik und Informatik, Universität Passau, Germany (e-mail: herrmann@fmi.uni-passau.delengauer@fmi.uni-passau.de)
CHRISTIAN LENGAUER
Affiliation:
Fakultät für Mathematik und Informatik, Universität Passau, Germany (e-mail: herrmann@fmi.uni-passau.delengauer@fmi.uni-passau.de)
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Abstract

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We present a hierarchical classification of specializations of the divide-and-conquer paradigm. The aim is to identify a subclass of divide-and-conquer algorithms with an efficient parallel implementation which can be viewed as a static space-time mapping. The specializations impose a balanced call tree, a fixed degree of the problem division, and elementwise operations. The correctness of our compile-time transformations is proved by equational reasoning in Haskell; recursion and iteration are handled by induction. We demonstrate the practicality of the skeleton by some examples, one of which is Strassen's matrix multiplication.

Type
Research Article
Copyright
1999 Cambridge University Press
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