 
Summary: Faster randomized consensus with an oblivious adversary
James Aspnes
February 15, 2012
Abstract
Two new algorithms are given for randomized consensus in a sharedmemory model with an
oblivious adversary. Each is based on a new construction of a conciliator, an object that guar
antees termination and validity, but that only guarantees agreement with constant probability.
The first conciliator assumes unitcost snapshots and achieves agreement among n processes
with probability 1  in O(log
n + log(1/ )) steps for each process. The second uses ordinary
multiwriter registers, and achieves agreement with probability 1  in O(log log n + log(1/ ))
steps. Combining these constructions with known results gives randomized consensus for ar
bitrarily many possible input values using unitcost snapshots in O(log
n) expected steps and
randomized consensus for up to O(log n log log n) possible input values using ordinary registers
in O(log log n) expected steps. The possibility of further improvement is considered.
Department of Computer Science, Yale University. Email: aspnes@cs.yale.edu. Supported in part by NSF
grant CCF0916389.
1 Introduction
