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 - 2005/1/1
Y1 - 2005/1/1
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=24944576592&partnerID=8YFLogxK
U2 - 10.1007/11429647_11
DO - 10.1007/11429647_11
M3 - Conference article
AN - SCOPUS:24944576592
VL - 3499
SP - 115
EP - 126
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
SN - 0302-9743
T2 - 12 International Colloquium on Structural Information and Communication Complexity, SIROCCO 2005
Y2 - 24 May 2005 through 26 May 2005
ER -