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Surrounding Theorem: Developing Parallel Programs for Matrix-Convolutions

  • Kento Emoto
  • Kiminori Matsuzaki
  • Zhenjiang Hu
  • Masato Takeichi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4128)

Abstract

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. To solve this problem, we have proposed a skeletal framework on two-dimensional arrays based on the theory of constructive algorithmics. It supports users, even with little knowledge about parallel machines, to develop systematically both correct and efficient parallel programs on two-dimensional arrays. In this paper, we apply our framework to the matrix-convolutions often used in image filters and difference methods. We show the efficacy of the framework by giving a general parallel program for the matrix-convolutions described with the skeletons, and a theorem that optimizes the general program into an application-specific one.

Keywords

Binary Operator Parallel Program General Program Constructive Algorithmics Parallel Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kento Emoto
    • 1
  • Kiminori Matsuzaki
    • 1
  • Zhenjiang Hu
    • 1
  • Masato Takeichi
    • 1
  1. 1.Department of Mathematical InformaticsUniversity of Tokyo 

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