Two absolute bounds for distributed bit complexity

Authors:
Yefim Dinitz;Noam Solomon
Affiliations:
Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel;Dept. of Mathematics, Ben-Gurion University, Beer-Sheva, Israel
Venue:
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Year:
2005

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Exact communication costs for consensus and leader in a tree

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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).