Abstract
Two processors receive inputs X and Y respectively. The communication complexity of the function f is the number of bits (as a function of the input size) that the processors have to exchange to compute f(X,Y) for worst case inputs X and Y. The List-Non-Disjointness problem (X=(x 1,...,x n), Y=(y 1,...,y n), \(x^{j},y^{j}\in {\rm Z}^{n}_{2}\), to decide whether \(\exists_{j}x^{j}=y^{j}\)) exhibits maximal discrepancy between deterministic n 2 and Las Vegas (Θ(n)) communication complexity. Fleischer, Jung, Mehlhorn (1995) have shown that if a Las Vegas algorithm expects to communicate Ω(n logn) bits, then this can be done with a small number of coin tosses.
Even with an improved randomness efficiency, this result is extended to the (much more interesting) case of efficient algorithms (i.e. with linear communication complexity). For any R ∈ ℕ, R coin tosses are sufficient for O(n+n 2 /2R) transmitted bits.
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
Aho, A.V., Ullman, J.D., Yannakakis, M.: On notions of information transfer in VLSI circuits. In: Proceedings of the fifteenth annual ACM symposium on Theory of computing, pp. 133–139 (1983)
Lawrence Carter, J., Wegman, M.N.: Universal classes of hash functions. Journal of Computer and System Sciences 18(2), 143–154 (1979)
Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Math. Stat. 23, 493–509 (1952)
Fleischer, R.: Communication complexity of multi-processor systems. Information Processing Letters 30(2), 57–65 (1989)
Fleischer, R., Jung, H., Mehlhorn, K.: A communicationrandomness tradeoff for two-processor systems. Information and Computation 116(2), 155–161 (1995)
Fürer, M.: The power of randomness for communication complexity. In: Proceedings of the nineteenth annual ACM conference on Theory of computing, pp. 178–181. ACM Press, New York (1987)
Fürer, M.: Universal hashing in VLSI. In: Reif, J.H. (ed.) AWOC 1988. LNCS, vol. 319, pp. 312–318. Springer, Heidelberg (1988)
Mehlhorn, K., Schmidt, E.M.: Las Vegas is better than determinism in VLSI and distributed computing (extended abstract). In: Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, pp. 330–337 (1982)
Motwani, R., Raghavan, P.: Randomized algorithms. Cambridge University Press, Cambridge (1995)
Papadimitriou, C.H., Sipser, M.: Communication complexity. In: Proceedings of the fourteenth annual ACM symposium on Theory of computing, pp. 196–200 (1982)
Yao, C.: Some complexity questions related to distributive computing (preliminary report). In: Proceedings of the eleventh annual ACM symposium on Theory of computing, pp. 209–213 (1979)
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
Fürer, M. (2004). An Improved Communication-Randomness Tradeoff. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_48
Download citation
DOI: https://doi.org/10.1007/978-3-540-24698-5_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21258-4
Online ISBN: 978-3-540-24698-5
eBook Packages: Springer Book Archive