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 1.5n 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).
|Number of pages||12|
|Journal||Lecture Notes in Computer Science|
|State||Published - 1 Jan 2005|
|Event||12 International Colloquium on Structural Information and Communication Complexity, SIROCCO 2005 - Mont Saint-Michel, France|
Duration: 24 May 2005 → 26 May 2005