Abstract
The paradigm of quasirandomness led to dramatic progress in different areas of mathematics, with the invention of quasi-Monte Carlo methods in numerical integration probably being the best known example. In the last two decades, discrete mathematics heavily used quasirandom ideas, leading, e.g., to notions like quasirandom graphs.
We feel that it is now time to exploit quasirandomness in computer science. As a first application, we propose and analyze a quasirandom analogue of the classical randomized rumor spreading protocol to disseminate information in networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angelopoulos, S., Bläser, M., Doerr, B., Fouz, M., Huber, A., Panagiotou, K.: Quasirandom Rumor Spreading: Tight Bounds and the Value of Random Bits (submitted, 2009)
Aleliunas, R., Karp, R., Lipton, R., Lovász, L., Rackoff, C.: Random walks, universal traversal sequences, and the complexity of maze problems. In: 20th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 218–223 (1979)
Alon, N., Spencer, J.H.: The Probabilistic Method, 2nd edn. Wiley, Chichester (2000)
Berenbrink, P., Elsässer, R., Friedetzky, T.: Efficient randomized broadcasting in random regular networks with applications in peer-to-peer systems. In: 27th ACM Symposium on Principles of Distributed Computing (PODC), pp. 155–164 (2008)
Doerr, B., Friedrich, T., Künnemann, M., Sauerwald, T.: Quasirandom rumor spreading: An experimental analysis. In: Proceedings of the 10th Workshop on Algorithm Engineering and Experiments (ALENEX), pp. 145–153 (2009)
Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 773–781 (2008)
Doerr, B., Friedrich, T., Sauerwald, T.: Quasirandom rumor spreading: Expanders, push vs. pull, and robustness. In: Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP) (2009)
Demers, A.J., Greene, D.H., Hauser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H.E., Swinehart, D.C., Terry, D.B.: Epidemic algorithms for replicated database maintenance. Operating Systems Review 22, 8–32 (1988)
Elsässer, R.: On the communication complexity of randomized broadcasting in random-like graphs. In: 18th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 148–157 (2006)
Erdős, P.: Graph theory and probability. Canad. J. Math. 11, 34–38 (1959)
Elsässer, R., Sauerwald, T.: On the runtime and robustness of randomized broadcasting. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 349–358. Springer, Heidelberg (2006)
Elsässer, R., Sauerwald, T.: Broadcasting vs. Mixing and information dissemination on cayley graphs. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 163–174. Springer, Heidelberg (2007)
Elsässer, R., Sauerwald, T.: On the power of memory in randomized broadcasting. In: 19th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 218–227 (2008)
Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)
Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures and Algorithms 1, 447–460 (1990)
Heinrich, S., Novak, E., Wasilkowski, G.W., Woźniakowski, H.: The inverse of the star-discrepancy depends linearly on the dimension. Acta Arithmetica 96, 279–302 (2001)
Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: 44th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 482–491 (2003)
Karp, R., Schindelhauer, C., Shenker, S., Vöcking, B.: Randomized rumor spreading. In: 41st IEEE Symposium on Foundations of Computer Science (FOCS), pp. 565–574 (2000)
Matoušek, J.: Geometric Discrepancy. Springer, Berlin (1999)
Reingold, O.: Undirected ST-connectivity in log-space. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), pp. 376–385 (2005)
Robbins, H.: A remark on Stirling’s formula. American Mathematical Monthly 62, 26–29 (1955)
Sauerwald, T.: On mixing and edge expansion properties in randomized broadcasting. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 196–207. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Doerr, B. (2009). Introducing Quasirandomness to Computer Science. In: Albers, S., Alt, H., Näher, S. (eds) Efficient Algorithms. Lecture Notes in Computer Science, vol 5760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03456-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-03456-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03455-8
Online ISBN: 978-3-642-03456-5
eBook Packages: Computer ScienceComputer Science (R0)