Abstract
We consider the problem of deterministic broadcasting in undirected radio networks with limited topological information. We show that for every deterministic protocol there exists a radius 2 network which requires at least \(\Omega(n^{\frac{1}{2}})\) rounds for completing broadcast. The previous best lower bound for constant diameter networks is \(\Omega(n^{\frac{1}{4}})\) rounds, due to [23]. For networks of radius D the lower bound can be extended to \(\Omega((nD)^{\frac{1}{2}})\) rounds. This resolves the open problem posed by [23].
Of perhaps more interest is our approach for proving the lower bound which is novel. We quantify the amount of connectivity information, about the topology of the network, that the source can learn in arbitrary number of rounds of an a deterministic broadcasting protocol. This approach is much more intuitive and exposes the structure of the broadcasting problem. We believe it is of independent interest and may have other applications.
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References
Alon, N., Bar-Noy, A., Linial, N., Peleg, D.: A lower bound for radio broadcast. Journal of Computer Science and System Sciences 43, 290–298 (1991)
Awerbuch, B.: A new distributed depth-first-search algorithm. Information Processing Letters 20, 147–150 (1985)
Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time complexity of broadcast in radio networks: an exponential gap between determinism and randomization. Journal of Computer and System Sciences 45, 104–126 (1992)
Pelc, A.: Personal communication (November 2002)
Czumaj, A., Rytter, W.: Broadcasting Algorithms in Radio Networks with Unknown Topology. To appear in Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2003), Cambridge, MA (2003)
Bruschi, B., Del Pinto, M.: Lower bounds for the broadcast problem in mobile radio networks. Distr. Comp. 10, 129–135 (1997)
Chlamtac, I., Farago, A.: Making transmission schedule immune to topology changes in multi-hop packet radio networks. IEEE/ACM Trans. on Networking 2, 23–29 (1994)
Chlamtac, I., Weinstein, O.: The wave expansion approach to broadcasting in multihop radio networks. IEEE Trans. on Communications 39, 426–433 (1991)
Chelbus, B.S., Gasieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. In: 11th ACM-SIAM SODA, pp. 861–870
Chelbus, B.S., Gasieniec, L., Gibbons, A., Ostlin, A., Robson, J.M.: Deterministic radio broadcasting. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 717–728. Springer, Heidelberg (2000)
Chrobak, M., Gasieniec, L., Rytter, W.: Fast broadcasting and gossiping in radio networks. In: Proc. 41st Symposium an Foundations of Computer Science (FOCS 2000), pp. 575–581 (2000)
Clementi, A.E.F., Monti, A., Silvestri, R.: Selective families, superimposed codes, and broadcasting on unknown radio networks. In: Proc. 12th Ann. ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 709–718 (2001)
Cruz, R., Hajek, B.: A new upper bound to the throughput of a multi-access broadcast channel. IEEE Trans. Inf. Theory IT-28(3), 402–405 (1982)
De Marco, G., Pelc, A.: Faster broadcasting in unknown radio networks. Information Processing Letter 79, 53–56 (2001)
Erdös, P., Frankl, P., Furedi, Z.: Families of finite sets in which no set is covered by the union of r others. Israel Journal of Math. 51, 79–89 (1985)
Gabour, I., Mansour, Y.: Broadcast in radio networks. In: Proc. 6th Ann. ACMSIAM Symp. on Discrete Algorithms (SODA 1996), pp. 577–585 (1996)
Hwang, F.K.: The time complexity of deterministic broadcast in radio networks. Discrete Applied Mathematics 60, 219–222 (1995)
Indyk, P.: Explicit constructions of selector and related combinatorial structures, with applications. In: Proc. 13th Ann. ACM-SIAM Symposium on Disceret Algorithms (SODA 2002), pp. 697–704 (2002)
Kauz, W.H., Singleton, R.R.C.: Nonrandom binary superimposed codes. IEEE Trans. on Information Theory 10, 363–377 (1964)
Kushilevitz, E., Mansour, Y.: An Ω(Dlog(N/D)) lower bound for broadcast in radio networks. SIAM J. on Computing 27, 702–712 (1998)
M.: MOLLE, Unifications and extensions of the multiple access communications problem. Ph.D. Thesis, University of California, Los Angeles, Los Angeles, Calif. (July 1981)
Reingold, O., Vadhan, S., Wigderson, A.: Entropy waves, the zig-zag product, and new constant degree expanders and extractors. In: Proc. 41st Symposium on Foundations of Computer Science (FOCS 2000), pp. 3–13 (2000)
Kowalski, D.R., Pelc, A.: Deterministic Broadcasting Time in Radio Networks of Unknown Topology. Accepted to Proc. 43rd Symposium on Foundations of Computer Science (FOCS 2002) (2002)
Li, M., Vitanyi, P.: Introduction to Kolmogorov Complexity and it’s applications, 2nd edn. Springer, Heidelberg
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Series in Telecommunications (1990)
Errata regarding ”On the Time-Complexity of Broadcast in Radio Networks: An Exponential Gap Between Determinism and Randomization” (December 2002), available from http://www.wisdom.weizmann.ac.il/oded/pbgi.html
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Brito, C., Gafni, E., Vaya, S. (2004). An Information Theoretic Lower Bound for Broadcasting in Radio Networks. 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_47
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DOI: https://doi.org/10.1007/978-3-540-24749-4_47
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