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A trade-off between information and communication in broadcast protocols

Authors:

Baruch Awerbuch,

Oded Goldreich,

David PelegAuthors Info & Claims

Journal of the ACM (JACM), Volume 37, Issue 2

Pages 238 - 256

https://doi.org/10.1145/77600.77618

Published: 01 April 1990 Publication History

Abstract

This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. The widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors but does not know the entire network topology, is assumed. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before.

It is shown that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires Θ(↿V↾) messages, where V is the set of processors in the network. It is proved that, if one counts messages of bounded length, then broadcast requires Θ(↿E↾) messages, where E is the set of edges in the network.

Assuming an intermediate model in which each vertex knows the topology of the network in radius ρ ≥ 1 from itself, matching upper and lower bounds of Θ(min{↿E↾, ↿V↾^1+Θ(l)/ρ}) is proved on the number of messages of bounded length required for broadcast. Both the upper and lower bounds hold for both synchronous and asynchronous network models.

The same results hold for the construction of spanning trees, and various other global tasks.

References

[1]

ABRAHAMSON, K., ADLER, A., HIGHAM, L., AND KIRKPATRICK, D. Probabilistic solitude verification on a ring. In Proceedings of the 5th Annual ACM Symposium on Principles of Distributed Computing. ACM, New York, 1986, pp. 161-173.

[2]

AFEK, Y., AND GAFNI, E. 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, Ont., Canada, Aug. 5-7). ACM, New York, 1985, pp. 186-195.

[3]

ATTIYA, C., SNIR, M., AND WARMUTH, M. Computing on anonymous ring. In Proceedings of the 4th Annual ACM Symposium on Principles of Distributed Computing (Minaki, Ont., Canada, Aug. 5-7). ACM, New York, 1985, pp. 196-203.

[4]

AWERBUCH, B. Complexity of network synchronization. J. ACM 32, 4 (Oct. 1985), 804-823.

[5]

AWERBUCH, B., GOLDREICH, O., AND VAINISH, R. O1"1 the message complexity of broadcast: A basic lower bound. Tech. Memo MIT/LCS/TM-325. MIT, Cambridge, Mass., April 1987.

[6]

BOLLOBAS, B. Extremal Graph Theory. Academic Press, Orlando, Fla., 1978.

[7]

BURNS, J.E. A formal model for message passing systems. Tech. Rep. TR-9 l. Indiana University, Bloomington, Ind., 1980.

[8]

DALAL, Y. K., AND METCALFE, R. Reserve path forwarding of broadcast packets. Commun. ACM 21, I2 (1978), 1040-1048.

[9]

EVEN, S. Graph Algorithms. Computer Science Press, Potomac, Md., 1979.

[10]

FREDERICKSON, G.R. Trade-offs for selection in distributed networks. In Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing. ACM, New York, 1983, pp. 154-I60.

[11]

FREDERICKSON, G. R., AND LYNCH, N.A. 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. ACM, New York, 1984, pp. 493-503.

[12]

GALLAGER, R. G., HUMBLET, P. A., AND SPIRA, P. M. A distributed algorithm for minimumweight spanning trees. ACM Trans. Frog. Lang. Syst. 5, 1 (Jan. 1983), 66-77.

[13]

GOLDREICH, O., AND SHRIRA, L. The effects of link failures on computations in asynchronous rings. In Proceedings of the 5th Annual ACM Symposium on Principles of Distributed Computing. ACM, New York, 1986, pp. 174-186.

[14]

GRAHAM, R. L., ROTHSCHILD, B. L., AND SPENCER, J. H. Ramsey Theory. Wiley, New York, I980.

[15]

KORACH, E., MORAN, S., AND ZAKS, S. Tight lower and upper bounds for some distributed algorithms for complete network of processors, in Proceedings of the 3rd Annual Symposium on Principles of Distributed Computing (Vancouver, B.C., Canada, Aug. 27-29). ACM, New York, 1984, pp. 199-207.

[16]

KORACH, E., MORAN, S., AND ZAKS, S. The optimality of distributed constructions of minimum weight and degree restricted spanning trees in a complete network of processors. In Proceedings of the 4th Annual ACM Symposium on Principles of Distributed Computing (Minaki, Ont., Canada, Aug. 5-7). ACM, New York, 1985, pp. 277-286.

[17]

LYNCH, N. A., AND FISCHER, M.J. On describing the behavior and implementation of distributed systems. Theoret. Comput. Sci. 13 ( 1981), 17-43.

[18]

MANSOUR, Y., AND ZAKS, S. On the bit complexity of distributed computation in a ring with a leader, in Proceedings of the 5th Annual ACM Symposium on Principles of Distributed Computing. ACM, New York, 1986, pp. 15 l- 160.

[19]

MORAN, S., AND WARMUTH, M. Gap theorems in distributed computing, in Proceedings of the 5th Annual ACM Symposium on Principles of Distributed Computing. ACM, New York, 1986, pp. 131-140.

[20]

PACHL, J., KORACH, E., AND ROTEM, O. A technique for proving lower bounds for distributed maximum-finding algorithms. In Proceedings of the 14th Annual ACM Symposium on Theory of Computing. ACM, New York, 1982, pp. 378-382.

[21]

PELEG, D., AND SCH.~EFER, A. Graph spanners. J. Graph Theory 13 (1989), 99-116.

[22]

REISCHUK, R., AND KOSHORS, M. Lower bound for synchronous systems and the advantage of local information, in Proceedings of the 2nd International Workshop on Distributed Algorithms (Amsterdam). Lecture Notes in Computer Science, vol. 312, Springer-Verlag, New York, June 1987.

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Reviews

Reviewer: William W. Oblitey

The discussions and proofs of the complexity of message broadcasting in distributed systems given here are based on point-to-point communication networks and then generalized to networks of arbitrary topology. The network is modeled by a simple undirected graph whose vertices represent network nodes and whose edges represent bidirectional communication channels operating between the nodes. The model assigns to each processor in the network only the knowledge of its own identity and the identity of its neighbors. All messages transmitted on the network are considered to be elementary or are broken into elementary messages. An elementary message is one that contains a constant number of bits and a constant number of vertex identities. The communication complexity of an algorithm is then the total number of messages transmitted in a worst-case execution of the communication protocol on the network. The authors state the upper and lower bound complexities of broadcast messages and carefully take the reader through their proofs . This paper should appeal to people who have interests in the study and development of network protocols or in graph theory.

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cover image Journal of the ACM

Journal of the ACM Volume 37, Issue 2

April 1990

244 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/77600

Issue’s Table of Contents

Copyright © 1990 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1990

Published in JACM Volume 37, Issue 2

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