Summary: A modular approach to shared-memory consensus, with
applications to the probabilistic-write model
May 14, 2011
We show that consensus can be solved by an alternating sequence of adopt-commit ob-
jects [2, 25], which detect agreement, and conciliators, which ensure agreement with some
probability. We observe that most known randomized consensus algorithms have this structure.
We give a deterministic implementation of an m-valued adopt-commit object for an un-
bounded number of processes that uses lg m + (log log m) space and individual work. We also
give a randomized conciliator for any number of values in the probabilistic-write model with
n processes that guarantees agreement with constant probability while using one multi-writer
register, O(log n) expected individual work, and (n) expected total work. Combining these
objects gives a consensus protocol for the probabilistic-write model that uses O(log m + log n)
individual work and O(n log m) total work. No previous protocol in this model uses sublinear
individual work or linear total work for constant m.
The consensus problem  is to devise a protocol so that n processes, each with a private input,
can agree on a single common output that is equal to some process's input. For asynchronous