Tight Bounds for Anonymous Adopt-Commit Objects

摘要

We give matching upper and lower bounds of Θ (min ((log m)/(log log m); n)) 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 weak conflict-detectors. It follows that the same lower bound holds on the individual step complexity of m-valued wait-free anonymous consensus, even for randomized algorithms with global coins against an oblivious adversary. The upper bound can also be used to slightly improve the cost of randomized consensus in the probabilistic-write model.