With the increasing popularity of parallel programming environments such as PC clusters, more and more sequential programmers, with little knowledge about parallel architectures and parallel programming, are hoping to write parallel programs. Numerous attempts have been made to develop high-level parallel programming libraries that use abstraction to hide low-level concerns and reduce difficulties in parallel programming. Among them, libraries of parallel skeletons have emerged as a promising way towards this direction. Unfortunately, these libraries are not well accepted by sequential programmers, because of incomplete elimination of lower-level details, ad-hoc selection of library functions, unsatisfactory performance, or lack of convincing application examples. This paper addresses principle of designing skeleton libraries of parallel programming and reports implementation details and practical applications of a skeleton library SkeTo. The SkeTo library is unique in its feature that it has a solid theoretical foundation based on the theory of Constructive Algorithmics, and is practical to be used to describe various parallel computations in a sequential manner.

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Skeletal parallel programming is a promising approach to easy parallel programming in which users can build parallel programs simply by combining parts of a given set of ready-made parallel computation patterns called skeletons. There is a trade-off for this easiness in the form of an efficiency problem caused by the compositional style of the programming. One solution to this problem is fusion transformation that optimizes naively composed skeleton programs by eliminating redundant intermediate data structures. Several parallel skeleton libraries have automatic fusion mechanisms. However, there have been no automatic fusion mechanisms proposed for variable-length list (VLL) skeletons, even though such skeletons are useful for practical problems. The main difficulty is that previous fusion mechanisms are not applicable to VLL skeletons, and so the fusion cannot be completed. In this paper, we propose a novel fusion mechanism for VLL skeletons that can achieve both an easy programming interface and complete fusion. The proposed mechanism has been implemented in our skeleton library, SkeTo, by using the expression templates technique, experimental results have shown that it is very effective.

Computations on two-dimensional arrays such as matrices and images are one of the most fundamental and ubiquitous things in computational science and its vast application areas, but development of efficient parallel programs on two-dimensional arrays is known to be hard. In this paper, we propose a compositional framework that supports users, even with little knowledge about parallel machines, to develop both correct and efficient parallel programs on dense two-dimensional arrays systematically. The key feature of our framework is a novel use of the abide-tree representation of two-dimensional arrays. The presentation not only inherits the advantages of tree representations of matrices where recursive blocked algorithms can be defined to achieve better performance, but also supports transformational development of parallel programs and architecture-independent implementation owing to its solid theoretical foundation -the theory of constructive algorithmics.

Abstract.A new approach for fast parallel reductions on trees over distributed memory environments is proposed. By employing serialized trees as the data representation, our algorithm has a communication-efficient BSP implementation regardless of the shapes of inputs. The prototype implementation supports its real efficacy.

We show that MapReduce, the de facto standard for large scale data-intensive parallel programming, can be equipped with a programming theory in calculational form. By integrating the generate-and-test programming paradigm and semirings for aggregation of results, we propose a novel parallel programming framework for MapReduce. The framework consists of two important calculation theorems: the shortcut fusion theorem of semiring homomorphisms bridges the gap between specifications and efficient implementations, and the filterembedding theorem helps to develop parallel programs in a systematic and incremental way.

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