skip to main content
article
Open Access

A modular technique for the design of efficient distributed leader finding algorithms

Published:03 January 1990Publication History
Skip Abstract Section

Abstract

A general, modular technique for designing efficient leader finding algorithms in distributed, asynchronous networks is developed. This technique reduces the problem of efficient leader finding to a simpler problem of efficient serial traversing of the corresponding network. The message complexity of the resulting leader finding algorithms is bounded by [f(n) + n)(log2k + 1) (or (f(m) + n)(log2k + 1)], where n is the number of nodes in the network [m is the number of edges in the network], k is the number of nodes that start the algorithm, and f (n) [f(m)] is the message complexity of traversing the nodes [edges] of the network. The time complexity of these algorithms may be as large as their message complexity. This technique does not require that the FIFO discipline is obeyed by the links. The local memory needed for each node, besides the memory needed for the traversal algorithm, is logarithmic in the maximal identity of a node in the network. This result achieves in a unified way the best known upper bounds on the message complexity of leader finding algorithms for circular, complete, and general networks. It is also shown to be applicable to other classes of networks, and in some cases the message complexity of the resulting algorithms is better by a constant factor than that of previously known algorithms.

References

  1. 1 AFEK, Y., AND GAFNI, A. Time and message bounds for election in synchronous and asynchronous complete networks. In Proceedings of the 4th Annual ACM Symposium on Principles of Distributed Computing (Minaki, Canada, Aug. 1985), pp. 186-195. Google ScholarGoogle Scholar
  2. 2 BURNS, J.E. A formal model for message passing systems. Tech. Rep. TR-91, Indiana University, Sept. 1980.Google ScholarGoogle Scholar
  3. 3 BOUGE, L., AND FRANCEZ, N. A compositional approach to superimposition. In Proceedings of the 15th Annual ACM Symposium on the Principles of Programming Languages (San Diego, Calif., Jan. 1988), pp. 240-249. Google ScholarGoogle Scholar
  4. 4 DOLEV, D., KLAWE, M., AND RODEH, M. An O(nlogn) unidirectional distributed algorithm for extrema finding in a circle. J. Algorithms 3 (1982), 245-260.Google ScholarGoogle Scholar
  5. 5 EVEN, S. Graph Algorithms. Computer Science Press, 1979. Google ScholarGoogle Scholar
  6. 6 FREDRICKSON, C., AND LYNCH, N. The impact of synchronous communication on the problem of electing a leader in a ring. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing (Washington, D.C., 1984), pp. 493-503. Google ScholarGoogle Scholar
  7. 7 GAFNI, E., AND AFEK, Y. Election and traversal in unidirectional networks. In Proceedings of the 3rd Annual ACM Symposium on Principles of Distributed Computing (Vancouver, B.C., Canada, Aug. 1984), pp. 190-198. Google ScholarGoogle Scholar
  8. 8 GAFNI, E., AND AFEK, Y. Simple and efficient distributed algorithms for election in complete networks. In Proceedings of the 22nd Annual Allerton Conference on Communication, Control, and Computing (Monticello, Ill., Oct. 1984), pp. 689-698.Google ScholarGoogle Scholar
  9. 9 GAFNI, E., AND KORFHAGE, W. Distributed election in unidirectional Eulerian networks. In Proceedings of the 22nd Annual Allerton Conference on Communication, Control, and Computing (Monticello, Ill., Oct. 1984), pp. 699-700.Google ScholarGoogle Scholar
  10. 10 GALLAGER, R.G. Choosing a leader in a network. Unpublished memorandum, M.I.T., Cambridge, Mass., 1977.Google ScholarGoogle Scholar
  11. 11 GALLAGER, R.G. Finding a leader in networks with O(E) + O(NlogN) messages. Internal Memo., M.I.T., Cambridge, Mass., 1978.Google ScholarGoogle Scholar
  12. 12 GALLAGER, R. G., HUMBLET, P. M., AND SPIRA, P.M. A distributed algorithm for minimumweight spanning trees. ACM Trans. Program. Lang. Syst. 5, I (Jan. 1983), 66-77. Google ScholarGoogle Scholar
  13. 13 H{RSHBERG, D. S., AND SINCLAIR, J. $. Decentralized extrema-findingin circular configurations of processors. Commun. ACM 23, 11 (Nov. 1980), 627-628. Google ScholarGoogle Scholar
  14. 14 HUMBLET, P. Selecting a leader in a clique in O(nlogn) messages. Intern. Memo., Laboratory for Information and Decision Systems, M.I.T., Cambridge, Mass., 1984.Google ScholarGoogle Scholar
  15. 15 KORACH, E., AND MARKOVlTZ, M. Algorithm for distributed spanning tree construction in dynamic networks. Tech. Rep. 401, Dept. Computer Science, Technion, Haifa, Israel, Feb. 1986.Google ScholarGoogle Scholar
  16. 16 KORACU, E., MORAN, S., AND ZAKS, S. Tight lower and upper bounds for some distributed algorithms for a complete network of processors. In Proceedings of the 3rd Annual ACM Symposium on Principles of Distributed Computing (Vancouver, B.C., Canada, Aug. 1984), pp. 199-207. Google ScholarGoogle Scholar
  17. 17 KORACH, E., ROTEM, D., AND SANTORO, N. A probabilistic algorithm for decentralized extremafinding in a circular configuration of processors. Tech. Rep., University of Waterloo, Ont., Canada, 1981.Google ScholarGoogle Scholar
  18. 18 KORACH, E., ROTEM, D., AND SANTORO, N. Distributed algorithms for finding centers and medians in networks. ACM Trans. Program. Lang. Syst. 6, 3 (July 1984), 380-401. Google ScholarGoogle Scholar
  19. 19 KUTTEN, S. A unified approach to the efficient construction of distributed leader-findingalgorithms. Presented at the IEEE International Conference on Communication and Energy, Montreal, Canada, Oct. 1984.Google ScholarGoogle Scholar
  20. 20 KUTTEN, S. Traversing directed graphs--An upper and lower bound. Internal Memo., 1984.Google ScholarGoogle Scholar
  21. 21 LAVALLEE, I., AND ROUCAIROL, G. A fully distributed (minimal) spanning tree algorithm. Inf. Processing Lett. 23 (Aug. 1986), 55-62. Google ScholarGoogle Scholar
  22. 22 PACHL, J., KORACH, r., AND ROTEM, D. Lower bounds for distributed maximum-finding algorithms. J. ACM 31, 4 (Oct. 1984), 905-918. Google ScholarGoogle Scholar
  23. 23 PETERSON, G.L. An O(nlogn) unidirectional algorithm for the circular extrema problem. ACM{ Trans. Program. Lang. Syst. 4, 4 (Oct. 1982), 758-762. Google ScholarGoogle Scholar
  24. 24 SEGALL, A. Distributed network protocols. IEEE Trans. Inf. Theory IT-29, I (Jan. 1983), 23-35.Google ScholarGoogle Scholar
  25. 25 TANENBAUM, A.S. Computer Networks. Prentice-Hall, Englewood Cliffs, N.J., 1981. Google ScholarGoogle Scholar
  26. 26 TIWARI, P., AND LOUI, M. C. Simulation of chaotic algorithms by token algorithms. In Distributed Algorithms on Graphs, E. Gafni and N. Santoro, Eds. Carleton University Press, Northfield, Minn., 1986, pp. 145-152.Google ScholarGoogle Scholar
  27. 27 VITANYI, P. M.B. Distributed election in an Archimedean ring of processors. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing (Washington, D.C., 1984), pp. 542-547. Google ScholarGoogle Scholar

Index Terms

  1. A modular technique for the design of efficient distributed leader finding algorithms

                  Recommendations

                  Comments

                  Login options

                  Check if you have access through your login credentials or your institution to get full access on this article.

                  Sign in

                  Full Access

                  • Published in

                    cover image ACM Transactions on Programming Languages and Systems
                    ACM Transactions on Programming Languages and Systems  Volume 12, Issue 1
                    Jan. 1990
                    141 pages
                    ISSN:0164-0925
                    EISSN:1558-4593
                    DOI:10.1145/77606
                    Issue’s Table of Contents

                    Copyright © 1990 ACM

                    Publisher

                    Association for Computing Machinery

                    New York, NY, United States

                    Publication History

                    • Published: 3 January 1990
                    Published in toplas Volume 12, Issue 1

                    Permissions

                    Request permissions about this article.

                    Request Permissions

                    Check for updates

                    Qualifiers

                    • article

                  PDF Format

                  View or Download as a PDF file.

                  PDF

                  eReader

                  View online with eReader.

                  eReader