Skip to main content
SpringerLink
Log in

Honeycomb networks

  • Contributed Papers
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1995 (MFCS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 969))

Abstract

The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network. A honeycomb mesh network with n nodes has degree 3 and diameter ≈ 1.63√n −1, which is 25% smaller degree and 18.5% smaller diameter then the mesh connected computer with approximately the same number of nodes. A convenient addressing scheme for nodes is introduced which provides simple computation of shortest paths and the diameter. Simple and optimal (in the number of required communication steps) routing algorithm is developed. Vertex and edge symmetric honeycomb torus network is obtained by adding wrap around edges to the honeycomb mesh. The network cost, defined as the product of degree and diameter, is better for honeycomb networks than for the two other families based on square (mesh connected computers and tori) and triangular (hexagonal meshes and tori) tessellations. The average distance in honeycomb torus with n nodes is proved to be approximately 0.54√n.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akl S.G., The Design and Analysis of Parallel Algorithms, Prentice Hall, 1989.

    Google Scholar 

  2. Borgefors G., Distance transformations on hexagonal grids, Pattern recognition Letters, 9, 1989, 97–105.

    Google Scholar 

  3. Bell S.B.M., Holroyd F.C., and Mason D.C., A digital geometry for hexagonal pixels, Image and Vision Computing, 7, 1989, 194–204.

    Google Scholar 

  4. Chen M.S., Shin K.G., and Kandlur D.D., Addressing, routing, and broadcasting in hexagonal mesh multiprocessors, IEEE Trans. on Comp., 39, 1, 1990, 10–18.

    Google Scholar 

  5. Duncan R., A survey of parallel computer architectures, IEEE Survey & Tutorial Series, 30–31, 1990.

    Google Scholar 

  6. J. W. Dolter J.W., Ramanathan P. and Shin K. G., Performance Analysis of Virtual Cut-Through Switching in HARTS: A Hexagonal Mesh Multicomputer, IEEE Transactions on Computers, 40, 6, 669–680, 1991.

    Google Scholar 

  7. Gamst A., Homogeneous distribution of frequencies in a regular hexagonal cell system, IEEE Transactions on Vehicular Technology, 31, 3, 1982, 132–144.

    Google Scholar 

  8. D. Gordon D., I. Koren I., and Silberman G. M., Embedding Tree Structures in VLSI Hexagonal Arrays, IEEE Transactions on Computers, 33, 104–107, 1984.

    Google Scholar 

  9. Kumar V., Grama A., Gupta A., and Karypis G., Introduction to Parallel Computing, Design and Analysis of Algorithms, Benjamin/Cummings Company, Inc. 1994.

    Google Scholar 

  10. Lunnon W.F., Counting hexagonal and triangular polyominoes, in: Graph Theory and Computing (R.C. Read, ed.), Academic Press, 1972.

    Google Scholar 

  11. Lester L.N. and Sandor J., Computer graphics on a hexagonal grid, Computers and Graphics, 8, 1984, 401–409.

    Google Scholar 

  12. Martin A.J., The torus: an exercize in constructing a processing surface, Proc 2nd Caltech Conf. VLSI, 1981, 527–537.

    Google Scholar 

  13. Quinn M.J., Parallel Computing, Theory and Practice, McGraw and Hill, 1994.

    Google Scholar 

  14. Robic B. and Silc J., High-performance computing on a honeycomb architecture, Proc. 2nd Int. ACPC Parallel Computation Conf., LNCS, Austria, 1993.

    Google Scholar 

  15. Shin K.G., HARTS: A distributed real-time architecture, Computer, May 1991, 25–35.

    Google Scholar 

  16. Stojmenovic I., Honeycomb networks: Topological properties and communication algorithms, TR-95-01, Computer Science Department, University of Ottawa, January 1995.

    Google Scholar 

  17. Stevens K.S., Robinson S.V., and Davis A.L., The post office — communication support for distributed ensemble architectures, Proc. 6th Int. Conf. Distrib. Comput. Sys., 1986, 160–166.

    Google Scholar 

  18. Tosic R., Masulovic D., Stojmenovic I., Brunvoll J., Cyvin B.N. and Cyvin S.J., Enumeration of polyhex hydrocarbons to h=17, Journal of Chemical Information and Computer Sciences, 35, 1995, 181–187.

    Google Scholar 

  19. Trew A. and Wilson G. (ed.), Past, Present, Parallel, a Survey of Available Parallel Computing Systems, Springer-Verlag, 1991.

    Google Scholar 

  20. Yong-Kui L., The generation of circular arcs and straight lines on hexagonal grids, Computer Graphics Forum, 12, 1993, 21–32.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of Ottawa, K1N 9B4, Ottawa, Ontario, Canada

    Ivan Stojmenović

Authors
  1. Ivan Stojmenović
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jiří Wiedermann Petr Hájek

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stojmenović, I. (1995). Honeycomb networks. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_133

Download citation

  • DOI: https://doi.org/10.1007/3-540-60246-1_133

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60246-0

  • Online ISBN: 978-3-540-44768-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation