Massive parallelization of divide-and-conquer algorithms over powerlists

Achatz, Klaus; Schulte, Wolfram

doi:10.1016/0167-6423(95)00022-4

Cited by 9 publications

(5 citation statements)

References 17 publications

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“…Aside from Huang et al (1992), there is other work related to ours. Misra (1994) and Achatz and Schulte (1996) restrict themselves to a binary division of data and problems. The approach of Mou and Hudak (1988) and Mou (1989Mou ( , 1990 allows an arbitrary division of problems and a division of multi-dimensional data into two parts per dimension.…”

Section: Results Related Work and Further Researchmentioning

confidence: 99%

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

Herrmann

Lengauer

1999

J. Funct. Prog.

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We propose a sequence of equational transformations and specializations which turns a divide-and-conquer skeleton in Haskell into a parallel loop nest in C. Our initial skeleton is often viewed as general divide-and-conquer. The specializations impose a balanced call tree, a xed degree of the problem division, and elementwise operations. Our goal is to select parallel implementations of divide-and-conquer via a space-time mapping, which can be determined at compile time. The correctness of our transformations is proved by equational reasoning in Haskell; recursion and iteration are handled by induction. Finally, we demonstrate the practicality of the skeleton by expressing Strassen's matrix multiplication in it.

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Section: Results Related Work and Further Researchmentioning

confidence: 99%

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

Herrmann

Lengauer

1999

J. Funct. Prog.

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“…Blelloch [4] gives an explicitly data parallel language that can express recursions in divide and conquer algorithms. Misra [19] describes the powerlist, a data structure akin to LISP list, but more suited for parallel algorithms and parallel recursions [1]. List homomorphisms are recursive functions on lists that can describe divide and conquer recursions and also map well to powerlists [11].…”

Section: Related Workmentioning

confidence: 99%

Optimizing the parallel computation of linear recurrences using compact matrix representations

Nistor

Chin

Tan

et al. 2009

Journal of Parallel and Distributed Computing

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“…We do not deal with the issue of mapping these programs to particular parallel architectures, nor provide suitable cost models to justify the synthesized programs. A number of other works, such as [AS96,PP93], have dealt with the more intricate implementation issue using divide-and-conquer programs as starting points. These works are therefore complimentary to our proposal.…”

Section: An] C) =~F= a +(C X N)mentioning

confidence: 99%

Deriving efficient parallel programs for complex recurrences

Teo

Chin

Tan

1997

Proceedings of the Second International Symposium on Parallel Symbolic Computation - PASCO '97

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We propose a method to synthesize parallel divideand-conquer programs from non-trivial sequential recurrences. 'Ikaditionally, such derivation methods are based on schematic rules which attempt to match each given sequential program to a prescribed set of program schemes that have parallel counterparts. Instead of relying on specialized program schemes, we propose a new approach to parallelization based on techniques built using elementary transformation rules.Our approach requires an induction to recover parallelism from sequential programs. To achieve this, we apply a second-order generalisation step to selected instances of sequent ial equations, before an inductive derivation procedure. The new approach is systematic enough to be semiautomated, and shall be shown to be widely applicable using a range of examples.

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Massive parallelization of divide-and-conquer algorithms over powerlists

Cited by 9 publications

References 17 publications

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

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

Optimizing the parallel computation of linear recurrences using compact matrix representations

Deriving efficient parallel programs for complex recurrences

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