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Introducing Quasirandomness to Computer Science

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Efficient Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5760))

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.

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References

  1. 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)

    Google Scholar 

  2. 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)

    Google Scholar 

  3. Alon, N., Spencer, J.H.: The Probabilistic Method, 2nd edn. Wiley, Chichester (2000)

    Book  MATH  Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. 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)

    Google Scholar 

  10. Erdős, P.: Graph theory and probability. Canad. J. Math. 11, 34–38 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. 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)

    Google Scholar 

  14. Frieze, A.M., Grimmett, G.R.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10, 57–77 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  15. Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. Random Structures and Algorithms 1, 447–460 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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)

    Article  MathSciNet  MATH  Google Scholar 

  17. 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)

    Google Scholar 

  18. 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)

    Google Scholar 

  19. Matoušek, J.: Geometric Discrepancy. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  20. Reingold, O.: Undirected ST-connectivity in log-space. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), pp. 376–385 (2005)

    Google Scholar 

  21. Robbins, H.: A remark on Stirling’s formula. American Mathematical Monthly 62, 26–29 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  22. 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)

    Chapter  Google Scholar 

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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

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  • 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

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