Abstract
In many large, distributed or mobile networks, broadcast algorithms are used to update information stored at the nodes. In this paper, we propose a new model of communication based on rendezvous and analyze a multi-hop distributed algorithm to broadcast a message in a synchronous setting. In the rendezvous model, two neighbors u and v can communicate if and only if u calls v and v calls u simultaneously. Thus nodes u and v obtain a rendezvous at a meeting point. If m is the number of meeting points, the network can be modeled by a graph of n vertices and m edges. At each round, every vertex chooses a random neighbor and there is a rendezvous if an edge has been chosen by its two extremities. Rendezvous enable an exchange of information between the two entities. We get sharp lower and upper bounds on the time complexity in terms of number of rounds to broadcast: we show that, for any graph, the expected number of rounds is between log n and O(n 2). For these two bounds, we prove that there exist some graphs for which the expected number of rounds is either O(log n) or Ω(n 2). For specific topologies, additional bounds are given.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Albers, S., Henzinger, M.: Exploring unknown environments. SIAM Journal on Computing 29(4), 1164–1188 (2000)
Angluin, D.: Local and global properties in networks of processors. In: Proceedings of the 12th Symposium on theory of computing, pp. 82–93 (1980)
Barriere, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Capture of an intruder by mobile agents. In: 14th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 200–209 (2002)
Bender, M.A., Slonim, D.K.: The power of team exploration: two robots can learn unlabeled directed graphs. In: Proceedings of the 35rd Annual Symposium on Foundations of Computer Science, pp. 75–85. IEEE Computer Society Press, Los Alamitos (1994)
Chlebus, B.: Randomized communication in radio networks. In: Handbook on Randomized Computing, Kluwer Academic, Dordrecht (to appear), http://citeseer.nj.nec.com/489613.html
Comellas, F., Ozón, J., Peters, J.G.: Deterministic small-world communication networks. Information Processing Letters 76(1-2), 83–90 (2000)
Deng, X., Kameda, T., Papadimitriou, C.H.: How to learn an unknown environment i: The rectilinear case. Journal of the ACM 45(2), 215–245 (1998)
Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures and Algorithms 1 (1990)
Habib, M., McDiarmid, C., Ramirez-Alfonsin, J., Reed, B. (eds.): Probabilistic Methods for Algorithmic Discrete Mathematics. Springer, Heidelberg (1998)
Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18, 319–349 (1988)
Karp, R.M., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: IEEE Symposium on Foundations of Computer Science, pp. 565–574 (2000)
Lynch, N.: A hundred impossibility proofs for distributed computing. In: Proceedings of the 8th ACM Symposium on Principles of Distributed Computing (PODC), pp. 1–28. ACM Press, New York (1989)
Metivier, Y., Saheb, N., Zemmari, A.: Randomized rendezvous. Trends in mathematics, pp. 183–194 (2000)
Metivier, Y., Saheb, N., Zemmari, A.: Randomized local elections. Information processing letters 82, 313–320 (2002)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge Univ. Press, Cambridge (1995)
Rao, N., Kareti, S., Shi, W., Iyenagar, S.: Robot navigation in unknown terrains: Introductory survey of non-heuristic algorithms (1993), http://citeseer.nj.nec.com/rao93robot.html
Tel, G.: Introduction to distributed algorithms. Cambridge University Press, Cambridge (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Duchon, P., Hanusse, N., Saheb, N., Zemmari, A. (2004). Broadcast in the Rendezvous Model. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_49
Download citation
DOI: https://doi.org/10.1007/978-3-540-24749-4_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21236-2
Online ISBN: 978-3-540-24749-4
eBook Packages: Springer Book Archive