Elsevier

Parallel Computing

Volume 22, Issue 14, March 1997, Pages 2047-2064
Parallel Computing

A family of network topologies with multiple loops and logarithmic diameter

https://doi.org/10.1016/S0167-8191(97)00067-7Get rights and content

Abstract

A new family of network topologies containing multiple loops is discussed in this paper. In the proposed structure, N processors are interconnected to form a graph G(m, N), m ⩾ 3, where m is a parameter of the graph such that N is an even multiple of m and (m − 1) × 2[(m− l)/2]+ < N ⩽ m × 2[m/2]+1. The graph G(m, N) is hamiltonian with an average node degree (3 + l/m), when m is even and exactly 3 when m is odd. Whereas, the maximum node degree is 4. The diameter of G(m, N) is upper bounded by [11m/8]+ 1. A point to point routing algorithm has been presented. Implementation of ASCEND/DESCEND algorithms in O(m) time has been discussed. It has been shown that in case of a single node failure, the diameter increases by at most 6.

References (14)

  • R.K. Das et al.

    Optimal communication algorithms in distributed loop networks

    J. Parallel Distributed Computing

    (1995)
  • S.G. Akl
  • S. Arno et al.

    Signed digit representation of minimal Hamming weight

    IEEE Trans. Comput.

    (1993)
  • B.W. Arden et al.

    Analysis of chordal ring network

    IEEE Trans. Comput.

    (1981)
  • J.C. Bermond et al.

    Minimal diameter double-loop networks: Dense optimal families

    Networks

    (1991)
  • F.T. Boesch et al.

    Circulants and their connectivities

    J. Graph Theory

    (1984)
  • P.J. Davis
There are more references available in the full text version of this article.

Cited by (0)

View full text
Copyright © 1997 Published by Elsevier B.V.