Distributed computing on transitive networks: The torus

  • Paul W. Beame
  • Hans L. Bodlaender
Contributed Papers Distributed Computing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 349)


We identify the class of transitive networks as being of particular interest for distributed computation with known topology. This class includes the ring and the complete network as well as the 2-dimensional grid network with boundary connections, i.e. the torus. We consider the bit and message complexity of computing non-constant functions on an asynchronous torus where processors are identical except that they have one input bit. We show that every function can be computed with bit complexity O(nn) on an √n × √n torus and show that this bound is optimal for many functions including AND, OR and XOR. We also give non-constant functions with a bit complexity linear in the number of processors on the torus. These bounds are better than those possible for the ring network.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Attiya and M. Snir. Better Computing on the Anonymous Ring. IBM Tech. Rep., IBM Research Division, Yorktown Heights, NY, 1988.Google Scholar
  2. [2]
    H. Attiya, M. Snir, and M. Warmuth. Computing on an anonymous ring. In Proc. 4th Ann ACM Symp. Principles of Distributed Computing, pages 196–203, 1985.Google Scholar
  3. [3]
    H. Bodlaender, S. Moran, and M. Warmuth. The inherent complexity of asynchronous computations on non-anonymous rings. 1987. Draft paper.Google Scholar
  4. [4]
    P. Duris and Z. Galil. Two lower bounds in asynchronous distributed computations. In Proc. 28th Ann. IEEE Symp. on Foundations of Comp. Science, pages 326–330, 1987.Google Scholar
  5. [5]
    S. Moran and M. Warmuth. Gap theorems for distributed computations. In Proc. 5th Ann ACM Symp. Principles of Distributed Computing, pages 131–140, 1986.Google Scholar
  6. [6]
    G. L. Peterson. Efficient Algorithms for Elections in Meshes and Complete Networks. Technical Report TR 140, Dept. of Comp. Science, Univ. of Rochester, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Paul W. Beame
    • 1
  • Hans L. Bodlaender
    • 2
  1. 1.Computer Science DepartmentUniversity of Washington, Sieg HallSeattleUSA
  2. 2.Department of Computer ScienceUniversity of UtrechtUtrechtThe Netherlands

Personalised recommendations