Analysis of distributed algorithms based on recurrence relations

Preliminary version
  • Yossi Malka
  • Sergio Rajsbaum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 579)


Recurrence relations of a certain type and their connection to Marked Graphs are studied. We show that these recurrence relations provide a paradigm which unifies distributed algorithms like synchronizers and distributed schedulers under a common formalism. This paradigm provides a technique for studying the properties of these algorithms when they are used in networks where link delays are not necessarily equal. We use the paradigm to analyze the performance of these algorithms. In particular it is shown that the behavior of algorithms which can be described by the recurrence relations is periodic after a short transitory phase and that the rate of computation can be computed efficiently.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Awerbuch, “Complexity of Network Synchronization,” J. of the ACM, Vol. 32, No. 4, Oct. 1985, pp. 804–823.Google Scholar
  2. [2]
    B. Awerbuch, A. Baratz, D. Peleg, “Cost-Sensitive Analysis of Communication Protocols,” IEEE FOCS, 1990.Google Scholar
  3. [3]
    V. C. Barbosa and E. Gafni, “Concurrency in Heavily Loaded Neighborhood-Constrained Systems,” ACM Trans. on Programming Languages and Systems, Vol. 11, No 4, Oct. 1989, pp. 562–584.Google Scholar
  4. [4]
    R. Cuninghame-Green, Minimax Algebra, Lecture Notes in Economics and Mathematical Systems, No. 166, Springer-Verlag, 1979.Google Scholar
  5. [5]
    K. M. Chandy and L. Lamport, “Distributed Snapshots: Determining Global States of Distributed Systems,” ACM Trans. on Computer Systems, Vol. 3, No 1, Feb. 1985.Google Scholar
  6. [6]
    F. Commoner, A.W. Holt, S. Even, A. Pnueli, “Marked Directed Graphs,” J. of Computer and System Sciences, Vol, vn5, No 5, Oct. 1971.Google Scholar
  7. [7]
    I. Chlamtac and S. Pinter, “Distributed nodes organization algorithm for channel access in a multi-hop dynamic radio network,” IEEE Trans. on Computers, vol. C-36, No. 6, June 1987, pp. 728–737.Google Scholar
  8. [8]
    S. Even, S. Rajsbaum, “Unison in Distributed Networks,” Sequences, Combinatorial, Compression, Security, and Transmission, R.M. Capocelli (ed.), Springer-Verlag, 1989. It is included in “Lack of a Global Clock Does not Slow Down the Computation in Distributed Networks,” TR-522, Department of Comp. Science, Technion, Haifa, Israel, October 1988.Google Scholar
  9. [9]
    S. Even, S. Rajsbaum, “The Use of a Synchronizer Yields Maximum Computation Rate in Distributed Networks,” Proc. 22th ACM STOC, 1990.Google Scholar
  10. [10]
    R. M. Karp, “A Characterization of the Minimum Cycle Mean in a Digraph,” Discrete Mathematics, Vol. 23, 1978, pp. 309–311.Google Scholar
  11. [11]
    S. Kirkpatrick, C.D. Gelatt, M.P, Vecchi, “Optimization by Simulated Annealing,” Science220 (4598), pp. 671–680 (May 13, 1983).Google Scholar
  12. [12]
    E.L. Lawler, Combinatorial Algorithms: Networks and Matroids, Holt, Rinehart, and Winston, 1976.Google Scholar
  13. [13]
    J. Malka, S. Moran, S. Zaks, “Analysis of a Distributed Scheduler for Communication Networks,” Technical Report # 495, Department of Computer Science, Technion, Haifa, Israel, Feb. 1988. Also in proceedings of the 3rd Agean Workshop on Computing, AWOC 88, Corfu, June 1988), LNCS, Vol 319, pp. 351–360, Springer Verlag, 1988.Google Scholar
  14. [14]
    Y. Ofek, I. Gopal, “Generating a Global Clock in a Distributed System,” IBM Research Report, 1987.Google Scholar
  15. [15]
    C.V. Ramamoorthy and G.S. Ho, “Performance Evaluation of asynchronous concurrent systems using Petri Nets,” IEEE Trans. Software Engineering, vol. SE-6, no. 5, pp. 440–449, (1980).Google Scholar
  16. [16]
    S. Rajsbaum, M. Sidi, “On the Average Performance of Synchronized Programs in Distributed Networks,” 4th Int. Workshop on Distributed Algorithms, Italy, October 1990, LNCS 486.Google Scholar
  17. [17]
    S. Rajsbaum, “Stochastic Marked Graphs,” to appear in 4th Int. Workshop on Petri Nets and Performance Models (PNPM91), Melbourn, Australia, Dec. 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Yossi Malka
    • 1
  • Sergio Rajsbaum
    • 2
  1. 1.IBM Science & TechnologyTechnion CityHaifaIsrael
  2. 2.Instituto de MatemáticasU.N.A.M.México

Personalised recommendations