TY - JOUR
T1 - Two absolute bounds for distributed bit complexity
AU - Dinitz, Yefim
AU - Solomon, Noam
N1 - Funding Information:
IPartially supported by the Lynn and William Frankel Center for Computer Science. ∗Corresponding author. Tel.: +972 8 647 7867; fax: +972 8 647 7650. E-mail addresses: dinitz@cs.bgu.ac.il (Y. Dinitz), noams@cs.bgu.ac.il (N. Solomon).
PY - 2007/10/1
Y1 - 2007/10/1
N2 - The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied the bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained there 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 suggested 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 presented lower bound proofs show that there is no optimal algorithm other than the suggested ones.
AB - The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied the bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained there 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 suggested 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 presented lower bound proofs show that there is no optimal algorithm other than the suggested ones.
KW - Absolute bound
KW - Bit complexity
KW - Distributed computing
KW - Leader election
UR - http://www.scopus.com/inward/record.url?scp=34548480467&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2007.04.027
DO - 10.1016/j.tcs.2007.04.027
M3 - Article
AN - SCOPUS:34548480467
SN - 0304-3975
VL - 384
SP - 168
EP - 183
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 2-3
ER -