Abstract
The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained open. The first is to close the gap between the known upper and lower bounds, for electing a leader by two linked processors. The second is whether the known algorithm, sending 1.5 n bits while electing a leader in a chain of even length n, is optimal, in the case when n is known to the processors. For both problems, absolutely exact bounds are found. Moreover, the lower bound proofs show that there is no optimal algorithm other than the suggested one(s).
Partially supported by the Lynn and William Frankel Center for Computer Science.
This is a preview of subscription content, log in via an institution to check access.
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
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics. McGraw–Hill, England (1998)
Dietzfelbinger, M.: The linear-array problem in communication complexity resolved. In: Proceedings of the 29th ACM Symposium on Theory of Computing, pp. 373–382 (1997)
Dinitz, Y., Moran, S., Rajsbaum, S.: Bit complexity of breaking and achieving symmetry in paths and rings. In: Proc. of the 31st Symposium on Theory of Computing, STOC 1999, pp. 265–274 (1999)
Dinitz, Y., Moran, S., Rajsbaum, S.: Bit complexity of breaking and achieving symmetry in chains and rings. Technical Report #CS-2004-11, Dept. of Comp. Sci., Technion, 29 p. (August 2004)
Dinitz, Y., Moran, S., Rajsbaum, S.: Exact Communication Costs for Consensus and Leader in a Tree. J. of Discrete Algorithms 1, 167–183 (2003)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers, Inc., San Francisco (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dinitz, Y., Solomon, N. (2005). Two Absolute Bounds for Distributed Bit Complexity . In: Pelc, A., Raynal, M. (eds) Structural Information and Communication Complexity. SIROCCO 2005. Lecture Notes in Computer Science, vol 3499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11429647_11
Download citation
DOI: https://doi.org/10.1007/11429647_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26052-3
Online ISBN: 978-3-540-32073-9
eBook Packages: Computer ScienceComputer Science (R0)