On the Performance of Parallel Matrix Factorisation on the Hypermesh

  • Authors:

  • A. Al-Ayyoub;M. Ould-Khaoua;K. Day

  • Affiliations:

  • Department of Computer Science and Information Systems, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan ayyoub@just.edu.jo;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK mohamed@dcs.gla.ac.uk;Department of Computer Science, Sultan Qaboos University, Sultanate of Oman kday@squ.edu.com

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2001

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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.