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On The SpaceTime Mapping Of A Class Of DivideAndConquer Recursions
, 1996
"... We propose a functional program skeleton for balanced fixeddegree divideandconquer and a method for its parallel implementation on messagepassing multiprocessors. In the method, the operations of the skeleton are first mapped to a geometric computational model which is then mapped to spacetime ..."
Abstract

Cited by 4 (3 self)
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We propose a functional program skeleton for balanced fixeddegree divideandconquer and a method for its parallel implementation on messagepassing multiprocessors. In the method, the operations of the skeleton are first mapped to a geometric computational model which is then mapped to spacetime in order to expose the inherent parallelism. This approach is inspired by the method of parallelizing nested loops in the polytope model. Keywords: divideandconquer, functional program, parallelization, skeleton, spacetime mapping. 1. Introduction The divideandconquer (DC) paradigm is a special case of cascading recursion which enables efficient solutions to many practical problems like the multiplication of matrices or large integers, Fast Fourier Transform, sorting, etc. We are interested in the parallelization of DC recursions with the goal of sublinear execution times on a mesh. Sublinearity can only be achieved if the input is read in parallel. We choose a mesh because it is a w...
From a Tabular Classication to Parallel Implementations of Linearly Recursive Functions
, 1997
"... We propose a classication for a set of linearly recursive functions, which can be expressed as instances of a skeleton for parallel linear recursion, and present new parallel implementations for them. This set includes well known higherorder functions, like Broadcast, Reduction and Scan, which we c ..."
Abstract
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We propose a classication for a set of linearly recursive functions, which can be expressed as instances of a skeleton for parallel linear recursion, and present new parallel implementations for them. This set includes well known higherorder functions, like Broadcast, Reduction and Scan, which we call basic components. Many compositions of these basic components are also linearly recursive functions; we present transformation rules from compositions of up to three basic components to instances of our skeleton. The advantage of this approach is that these instances have better parallel implementations than the compositions of the individual implementations of the corresponding basic components. Keywords: functional programming, linear recursion, parallelization, skeletons 1 Introduction Functional programming ooeers a very highlevel approach to specifying executable problem solutions. For example, the scheme of linear recursion can be expressed concisely as a higherorder function. I...