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Parallelization of DivideandConquer in the BirdMeertens Formalism
, 1995
"... . An SPMD parallel implementation schema for divideandconquer specifications is proposed and derived by formal refinement (transformation) of the specification. The specification is in the form of a mutually recursive functional definition. In a first phase, a parallel functional program schema is ..."
Abstract

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. An SPMD parallel implementation schema for divideandconquer specifications is proposed and derived by formal refinement (transformation) of the specification. The specification is in the form of a mutually recursive functional definition. In a first phase, a parallel functional program schema is constructed which consists of a communication tree and a functional program that is shared by all nodes of the tree. The fact that this phase proceeds by semanticspreserving transformations in the BirdMeertens formalism of higherorder functions guarantees the correctness of the resulting functional implementation. A second phase yields an imperative distributed messagepassing implementation of this schema. The derivation process is illustrated with an example: a twodimensional numerical integration algorithm. 1. Introduction One of the main problems in exploiting modern multiprocessor systems is how to develop correct and efficient programs for them. We address this problem using the ap...
NGraphs: A Topology for Parallel DivideandConquer on Transputer Networks
"... A parallel implementation of a divideandconquer template (skeleton) is derived systematically from its functional specification. The implementation makes use of a new processor topology for divideandconquer, called N graph, which suits transputer networks well: there are not more than 4 links p ..."
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A parallel implementation of a divideandconquer template (skeleton) is derived systematically from its functional specification. The implementation makes use of a new processor topology for divideandconquer, called N graph, which suits transputer networks well: there are not more than 4 links per processor, overlapping of computations and communication within a processor is exploited, the processor network is of an arbitrary fixed size, the load is balanced and all communications between processors are local. A parallel mergesort algorithm is used to illustrate the derivation process and the distributed parallel target program. Experimental results on a 64node transputer network are reported. 1 Introduction The wellknown technique of divideandconquer has been applied to a wide variety of problems. It is used when a problem solution can be defined recursively as a function of a collection of smaller instances of the same problem, generated from the description of the original ...