Advertisement

Algebraic constructions of efficient broadcast networks

  • Michael J. Dinneen
  • Michael R. Fellows
  • Vance Faber
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)

Abstract

Cayley graph techniques are introduced for the problem of constructing networks having the maximum possible number of nodes, among networks that satisfy prescribed bounds on the parameters maximum node degree and broadcast diameter. The broadcast diameter of a network is the maximum time required for a message originating at a node of the network to be relayed to all other nodes, under the restriction that in a single time step any node can communicate with only one neighboring node. For many parameter values these algebraic methods yield the largest known constructions, improving on previous graph-theoretic approaches. It has previously been shown that hypercubes are optimal for degree k and broadcast diameter k. A construction employing dihedral groups is shown to be optimal for degree k and broadcast diameter k + 1.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ABR]
    F. Annexstein, M. Baumslag and A. L. Rosenberg, “Group Action Graphs and Parallel Architectures,” SIAM Journal on Computing 19 (1990), 544–569.Google Scholar
  2. [BDQ]
    J-C. Bermond, C. Delorme and J. J. Quisquater, “Strategies for Interconnection Networks: Some Methods From Graph Theory,” Journal of Parallel and Distributed Computing 3 (1986), 433–449.Google Scholar
  3. [BDV]
    J. Bond, C. Delorme and W. F. de La Vega, “Large Cayley Graphs with Small Degree and Diameter,” Rapport de Recherche no. 392, LRI, Orsay, France, 1987.Google Scholar
  4. [BHLP1]
    J-C. Bermond, P. Hell, A. L. Liestman and J. G. Peters, “New Minimum Broadcast Graphs and Sparse Broadcast Graphs,” Technical Report CMPT 88-4, School of Computing Science, Simon Fraser University, B. C., Canada, 1988.Google Scholar
  5. [BHLP2]
    J-C. Bermond, P. Hell, A. L. Liestman and J. G. Peters, “Broadcasting in Bounded Degree Graphs,” Technical Report CMPT 88-5, School of Computing Science, Simon Fraser Uiversity, B. C., Canada, 1988.Google Scholar
  6. [CCD]
    D. V. Chudnovsky, G. V. Chudnovsky and M. M. Denneau, “Regular Graphs with Small Diameters as Models for Interconnection Networks,” Proceedings of the Third International Conference on Supercomputing (Boston, May 1988), 232–239.Google Scholar
  7. [CCDFFLMMS]
    L. Campbell, G. E. Carlsson, M. J. Dinneen, V. Faber, M. R. Fellows, M. A. Langston, J. W. Moore, A. P. Mullhaupt and H. B. Sexton, “Small Diameter Symmetric Networks from Linear Groups,” IEEE Transactions on Computers, to appear.Google Scholar
  8. [CCSW]
    G.E. Carlsson, J.E. Cruthirds, H.B. Sexton and C.G. Wright, “Interconnection Networks Based on Generalization of Cube-Connected Cycles,” IEEE Transactions on Computers, C-34 (1985), 769–777.Google Scholar
  9. [Ch]
    F. R. K. Chung, “Diameters of Graphs: Old Problems and New Results,” Congressus Numerantium 60 (1987), 295–317.Google Scholar
  10. [Di]
    M. J. Dinneen, “Algebraic Methods for Efficient Network Constructions,” Master's Thesis, Computer Science Department, University of Victoria, Victoria, B. C., Canada.Google Scholar
  11. [HHL]
    S. T. Hedetniemi, S. M. Hedetniemi and A. L. Liestman, “A Survey of Broadcasting and Gossiping in Communication Networks,” Networks 18 (1988), 319–349.Google Scholar
  12. [LP]
    A. L. Liestman and J. G. Peters, “Minimum Broadcast Digraphs,” Discrete Applied Mathematics, to appear.Google Scholar
  13. [LS]
    A. L. Liestman and H. Somani, “Post-Survey Broadcasting and Gossiping Papers,” manuscript, School of Computing Science, Simon Fraser University, B. C., Canada.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Michael J. Dinneen
    • 1
  • Michael R. Fellows
    • 1
  • Vance Faber
    • 2
  1. 1.Department of Computer ScienceUniversity of VictoriaVictoriaCanada
  2. 2.Los Alamos National LaboratoryLos AlamosUSA

Personalised recommendations