Combining shared-coin algorithms

This paper shows that shared coin algorithms can be combined to optimize several complexity measures, even in the presence of a strong adversary. By combining shared coins of Bracha and Rachman [10] and of Aspnes and Waarts [7], this yields a shared coin algorithm, and hence, a randomized consensus algorithm, with O(n log n) individual work and O(n log n) total work, using single-writer 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 failure-free executions, with one that takes O(log n) time in executions where at most √ n process fail, and another one O( n 3 n−f ) time in any other execution.