This Article 
 Bibliographic References 
 Add to: 
Distributed Computing on Regular Networks with Anonymous Nodes
February 1994 (vol. 43 no. 2)
pp. 211-218

Presents efficient algorithms for collecting information distributed among indistinguishable (anonymous) processors while performing certain operations on the information being collected. The efficiency objective is to minimize the communication-delay product and to obtain trade-offs between the two. The main contribution of the paper is a new efficient algorithm for performing sumlike operations (such as Abelian group operations and elementary symmetric functions) and the use of metrically regular graphs (which include the widely used hypercube interconnections) for information dissemination in distributed computations. The best algorithm has a communication-delay product of O(Nlog/sup 3/ N) (for W nodes), and obtaining an optimal /spl Omega/(Nlog/sup 2/N) algorithm remains an open problem.

[1] A. A. Albert and R. Sandler,An Introduction to Finite Projective Planes. New York: Holt, Rinehart and Winston, 1968.
[2] N. Alon, A. Barak, and U. Manber, "On disseminating information reliably without broadcasting," inProc. 7th Int. Conf. Distributed Computing Syst., 1987, pp. 74-81.
[3] D. Angluin, "Local and global properties in networks and processors," inProc. 12th Annual ACM Symp. Theory of Computing, 1980, pp. 82-93.
[4] H. Attiya, M. Snir, and M. K. Warmuth, "Computing on an anonymous ring,"J. ACM, vol. 35, no. 4, pp. 845-875, 1988.
[5] J.-C. Bermond, J. Bond, M. Paoli, and C. Peyrat, "Graphs and interconnection networks: Diameter and Vulnerability," inLecture Notes Series 82, Surveys in Combinatorics. London Mathematics Society, 1983.
[6] J.-C. Bermond, J-C. Konig, and M. Raynal, "General and efficient decentralized consensus protocols." inProc. 2nd Int. Workshop on Distributed Algorithms on Graphs, 1987.
[7] J.-C. Bermond and J-C. Konig, "General and efficient decentralized consensus protocols-II," inProc. Int. Workshop on Parallel and Distributed Syst., 1988, pp. 199-210.
[8] F. R. K. Chung, "Diameters of communication networks," inAMS Short Course on Mathematics of Information Processing, 1984.
[9] W. Feit and G. Higman, "The non-existence of certain generalized polygons,"J. Algebra, pp. 114-131, 1964.
[10] M. T. Heath, "Hypercube multiprocessors 1986,"SIAM, 1986.
[11] A. J. Hoffman and R. R. Singleton, "On Moore graphs with diameter 2 and 3,"IBM J. Res. Dev., vol. 4, pp. 497-504, 1960.
[12] G. A. Korn and T. M. Korn, "Section 1.4-3," inMathematical Handbook for Scientists and Engineers, New York: McGraw-Hill, 1968.
[13] E. Kranakis and D. Krizanc, "Distributed computing on anonymous hypercube networks," inProc. 3rd IEEE Symp. Parallel and Distributed Processing, 1991, pp. 722-729.
[14] T. V. Lakshman and A. K. Agrawala, "Efficient decentralized consensus protocols,"IEEE Trans. Software Eng., vol. SE-12, no. 5, pp. 600-607, May 1986.
[15] T. V. Lakshman and A. K. Agrawala, "Communication structure of decentralized commit protocols," inProc. 6th Int. Conf. Distributed Computing Syst., 1986, pp. 100-107.
[16] M. L. Neilsen and M. Mizuno, "Decentralized consensus protocols," inProc. 10th Annual Int. Phoenix Conf. on Computers and Communications, Mar. 1991, pp. 257-262.
[17] J. J. Rotman, "Theorem 4.6 (basis theorem)," inThe Theory of Groups: An Introduction. Newton, MA: Allyn and Bacon, 1973, p. 54.
[18] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 22-33, Jan. 1985.
[19] D. Skeen, "Nonblocking commit protocols," inProc. ACM SIGMOD Int. Conf. Management of Data, 1981, pp. 133-142.
[20] S. H. Son, "Efficient decentralized checkpointing in distributed database systems," inProc. 21st Int. Conf. Systems Sciences, 1988.
[21] S. M. Yuan and A. K. Agrawala, "A class of optimal decentralized commit protocols," inProc. 8th Int. Conf. Distrib. Computing Syst., 1988, pp. 234-241.

Index Terms:
hypercube networks; distributed algorithms; message passing; regular networks; anonymous nodes; distributed computing; communication-delay product; trade-off; efficiency objective; sumlike operations; information dissemination; distributed computations; distributed algorithms; finite projective planes; hypercubes; message complexity; metrically regular graphs; sparse graphs.
T.V. Lakshman, V.K. Wei, "Distributed Computing on Regular Networks with Anonymous Nodes," IEEE Transactions on Computers, vol. 43, no. 2, pp. 211-218, Feb. 1994, doi:10.1109/12.262125
Usage of this product signifies your acceptance of the Terms of Use.