 
Summary: Combining Shared Coin Algorithms
James Aspnes
Hagit Attiya
Keren Censor
Abstract
This paper shows that shared coin algorithms can be combined to optimize several complexity mea
sures, even in the presence of a strong adversary. By combining shared coins of Bracha and Rach
man [10] and of Aspnes and Waarts [7], this yields a shared coin algorithm, and hence, a randomized
consensus algorithm, with O(n log2
n) individual work and O(n2
log n) total work, using singlewriter
registers. This improves upon each of the above shared coins (where the former has a high cost for
individual work, while the latter reduces it but pays in the total work), and is currently the best for this
model.
Another application is to prove a construction of Saks, Shavit, and Woll [16], which combines a
shared coin algorithm that takes O(1) time in failurefree executions, with one that takes O(log n) time
in executions where at most
n process fail, and another one O( n3
nf ) time in any other execution.
