Abstract
We consider rumor spreading on random graphs and hypercubes in the quasirandom phone call model. In this model, every node has a list of neighbors whose order is specified by an adversary. In step i every node opens a channel to its ith neighbor (modulo degree) on that list, beginning from a randomly chosen starting position. Then, the channels can be used for bi-directional communication in that step. The goal is to spread a message efficiently to all nodes of the graph.
We show three results. For random graphs (with sufficiently many edges) we present an address-oblivious algorithm with runtime O(logn) that uses at most O(n log log n) message transmissions. For hypercubes of dimension log n we present an address-oblivious algorithm with runtime O(log n) that uses at most O(n (log log n)2) message transmissions. For hypercubes we also show a lower bound of Ω(n log n/log log n) on the total number of message transmissions required by any O(log n) time address-oblivious algorithm in the standard random phone call model. Together with a result of [8], our results imply that for random graphs and hypercubes the communication complexity of the quasirandom phone call model is significantly smaller than that of the standard phone call model. This seems to be surprising given the small amount of randomness used in our model.
The second author was partially supported by the German Research Foundation (DFG) under contract EL 399/2-1.
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References
Berenbrink, P., Elsässer, R., Friedetzky, T.: Efficient Randomised Broadcasting in Random Regular Networks with Applications in Peer-to-Peer Systems. In: Proc. of PODC 2008, pp. 155–164 (2008)
Berenbrink, P., Elsässer, R., Sauerwald, T.: Randomised Broadcasting: Memory vs. Randomness. In: Proc. of LATIN 2010 (to appear, 2010)
Bollobás, B.: Random Graphs. Academic Press, London (1985)
Chierichetti, F., Lattanzi, S., Panconesi, A.: Almost Tight Bounds for Rumour Spreading with Conductance. In: Proc. of STOC 2010 (to appear, 2010)
Demers, A., Greene, D., Hauser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H., Swinehart, D., Terry, D.: Epidemic algorithms for replicated database maintenance. In: Proc. of PODC 1987, pp. 1–12 (1987)
Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom Rumor Spreading. In: Proc. of SODA 2008, pp. 773–781 (2008)
Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading: expanders, push vs. pull, and robustness. In: Proc. of ICALP 2009, pp. 366–377 (2009)
Elsässer, R.: On the communication complexity of randomized broadcasting in random-like graphs. In: Proc. of SPAA 2006, pp. 148–157 (2006)
Elsässer, R., Sauerwald, T.: The power of memory in randomized broadcasting. In: Proc. of SODA 2008, pp. 218–227 (2008)
Erdős, P., Rényi, A.: On random graphs I. Publ. Math. Debrecen 6, 290–297 (1959)
Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures and Algorithms 1(4), 447–460 (1990)
Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)
Fountoulakis, N., Huber, A., Panagiotou, K.: Reliable broadcasting in random networks and the effect of density. In: Proc. of INFOCOM 2010 (to appear, 2010)
Hagerup, T., Rüb, C.: A guided tour of Chernoff bounds. Information Processing Letters 36(6), 305–308 (1990)
Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: Proc. of FOCS 2000, pp. 565–574 (2000)
McDiarmid, C.: On the method of bounded differences. In: Surveys in Combinatorics. London Math. Soc. Lectures Notes, vol. 141, pp. 148–188. Cambridge Univ. Press, Cambridge (1989)
Pittel, B.: On spreading rumor. SIAM Journal on Applied Mathematics 47(1), 213–223 (1987)
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Berenbrink, P., Elsässer, R., Sauerwald, T. (2010). Communication Complexity of Quasirandom Rumor Spreading. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_12
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DOI: https://doi.org/10.1007/978-3-642-15775-2_12
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