Summary: Tight Bounds for Adopt-Commit Objects
November 21, 2011
We give matching upper and lower bounds of min log m
log log m
for the space and individual step complexity of a wait-free m-valued adopt-
commit object implemented using multi-writer registers for n anonymous
processes. While the upper bound is deterministic, the lower bound holds
for randomized adopt-commit objects as well. Our results are based on
showing that adopt-commit objects are equivalent, up to small additive
constants, to a simpler class of objects that we call conflict detectors.
Our anonymous lower bound also applies to the individual step com-
plexity of m-valued wait-free anonymous consensus, even for randomized
algorithms with global coins against an oblivious adversary. The upper
bound can be used to slightly improve the cost of randomized consensus
in an oblivious-adversary model.
For non-anonymous deterministic implementations of adopt-commit