Advertisement

Algorithmica

, Volume 10, Issue 5, pp 383–398 | Cite as

A lower bound on the period length of a distributed scheduler

  • Yossi Malka
  • Shlomo Moran
  • Shmuel Zaks
Article

Abstract

Ad-scheduling of a graphG is a sequence of rounds, each consisting of some of the nodes of the graph, such that the distance between any two nodes participating in the same round is greater thand. Ad-scheduler is a protocol that determines ad-scheduling ofG. A 1-scheduler is applicable to process scheduling in a resource-sharing system, and to proper communication scheduling of the half-duplex model in communication networks. A 2-scheduler can be used as a collision-free protocol for radio networks.

In this paper a simpled-scheduler is analyzed. We first discuss basic properties of this scheduling, and give a complete characterization of this scheduling for trees and cycles. We study the period length of this scheduling, and the main result is a worst-case exponential lower bound for this length.

Key words

Distributed systems Schedulers Synchronizers Channel access protocols 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A]
    B. Awerbuch, Complexity of network synchronization,J. Assoc. Comput. Mach.,32 (1985), 804–823.Google Scholar
  2. [B]
    V. C. Barbosa, Concurrency in Systems with Neighborhood Constraints, Ph.D. Dissertation, Computer Science Department, University of California, Los Angeles, CA, 1986.Google Scholar
  3. [BG]
    V. C. Barbosa and E. Gafni, Concurrency in systems with neighborhood constraints,Proc. Conf. on Distributed Computing Systems, 1987, pp. 448–455.Google Scholar
  4. [CCGZ]
    C. T. Chou, I. Cidon, I. Gopal, and S. Zaks, Synchronizing Asynchronous Bounded Delay Networks, RC 12274, IBM T. J. Watson Research Center, Yorktown Heights, NY, October 1986.Google Scholar
  5. [CK]
    I. Chlamtac and S. Kutten, A spatial reuse TDMA/FDMA for mobile multi-hop radio networks,INFOCOM Conf. Proc., March 1985, pp. 385–393.Google Scholar
  6. [CM]
    K. M. Chandy and J. Misra, The drinking philosophers problem,ACM Trans. Program. Languages Systems,6(4) (1984), 632–646.Google Scholar
  7. [CP]
    I. Chlamtac and S. Pinter, Distributed nodes organization algorithm for channel access in a multiple-hop dynamic radio network,IEEE Trans. Comput.,36(6) (1987), 728–737.Google Scholar
  8. [CS]
    I. Cidon and M. Sidi, A Distributed Assignment Algorithm for Multi-Hop Packet-Radio Networks, RC 12563 (#56508), IBM Communications/Computer Science, IBM T. J. Watson Research Center, Yorktown Heights, NY, 1987.Google Scholar
  9. [E]
    S. Even,Graph Algorithms, Computer Science Press, Rockville, MD, 1979.Google Scholar
  10. [EGMT]
    S. Even, O. Goldreich, S. Moran, and P. Tong, On the NP-completeness of certain network testing problems,Networks,14 (1984), 1–24.Google Scholar
  11. [G]
    M. Golumbic,Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.Google Scholar
  12. [GB]
    E. Gafni and D. P. Bertsekas, Distributed algorithms for generating loop-free routes in networks with frequently changing topology,IEEE Trans. Comm.,29(1) (1985), 11–18.Google Scholar
  13. [GJ]
    M. R. Garey and D. S. Johnson,Computers and Interactability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA, 1979.Google Scholar
  14. [MMZ]
    Y. Malka, S. Moran, and S. Zaks, Analysis of a Distributed Scheduler for Communication Networks, Technical Report #495, Computer Science Department, Technion-Israel Institute of Technology, Haifa, Feb. 1988. An extended abstract appeared inProc. 3rd Agean Workshop on Computing, AWOC 88, Corfu, June 1988, Lecture Notes in Computer Science, Vol. 319, Springer-Verlag, Berlin, 1988, pp. 351–360.Google Scholar
  15. [MR]
    Y. Malka and S. Rasjbaum, Analysis of distributed algorithms based on recurrence relations,Proc. 5th International Workshop on Distributed Algorithms (WDAG), Delphi, Greece, October 1991 (S. Toueg, P. G. Spirakis, and L. Kirousis, eds.), Lecture Notes in Computer Science, Vol. 579, Springer-Verlag, Berlin, 1991, pp. 242–253.Google Scholar
  16. [NK]
    W. Narkiewitz and S. Kanematsu,Number Theory, World Scientific, Singapore, 1983.Google Scholar
  17. [SvL]
    A. A. Schoone and J. van Leeuwen, Simulation of Parallel Algorithms on a Distributed Network, Technical Report RUU-CS-86-1, Department of Computer Science, University of Utrecht, January 1986.Google Scholar
  18. [T]
    A. S. Tanenbaum,Computer Networks, Prentice-Hall, Englewood Cliffs, NJ, 1981.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Yossi Malka
    • 1
  • Shlomo Moran
    • 1
  • Shmuel Zaks
    • 1
  1. 1.Department of Computer ScienceTechnionHaifaIsrael

Personalised recommendations