James Aspnes and Faith Ellen. Tight bounds for adopt-commit objects. Submitted to Theory of Computing Systems (SPAA 2011 special issue), November 2011. An earlier version appeared in 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures, June 2011, pp. 317–324, under the title “Tight bounds for anonymous adopt-commit objects.”
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 conflict detectors.
Our anonymous lower bound also applies to the individual step complexity of m-valued wait-free anonymous consensus, 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 an oblivious-adversary model.
For non-anonymous deterministic implementations of adopt-commit objects, we show a lower bound of Ω(min(log m / log log m, sqrt(log n) / log log n) and an upper bound of O(min(log m / log log m, log n) on the worst-case individual step complexity.
@inproceedings{AspnesE2011,
author = {James Aspnes and Faith Ellen},
title = {Tight bounds for anonymous adopt-commit objects},
month = jun,
year = 2011,
pages={317--324},
booktitle={23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures}
}