On the performance of parallel matrix factorisation on the hypermesh

A. Al-Ayyoub*, M. Ould-Khaoua, K. Day

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Most common multicomputer networks, e.g. d-ary h-cubes, are graph topologies where an edge (channel) interconnects exactly two vertices (nodes). Hypergraphs are a generalisation of the graph model, where a channel interconnects an arbitrary number of nodes. Previous studies have used synthetic workloads (e.g. statistical distributions) to stress the superior performance characteristics of regular multi-dimensional hypergraphs, also known as hypermeshes, over d-ary h-cubes. There has been, however, hardly any study that has considered real-world parallel applications. This paper contributes towards filling this gap by providing a comparative study of the performance of one of the most common numerical problems, namely matrix factorisation, on the hypermesh, hypercube, and d-ary h-cube, To this end, the paper first introduces orthogonal networks as a unified model for describing both the graph and hypergraph topologies. It then develops a generalised parallel algorithm for matrix factorisation and evaluates its performance on the hypermesh, hypercube and d-ary h-cube. The results reveal that the hypermesh supports matrix computation more efficiently, and therefore provides more evidence of the hypermesh as a viable network for future large-scale multicomputers.

Original languageEnglish
Pages (from-to)37-53
Number of pages17
JournalJournal of Supercomputing
Volume20
Issue number1
DOIs
Publication statusPublished - Aug 2001

Keywords

  • Gaussian elimination
  • Hypermeshes
  • Interconnection networks
  • Matrix factorization
  • Multicomputers
  • Orthogonal networks
  • Performance analysis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture
  • Theoretical Computer Science
  • Computational Theory and Mathematics

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