Tight bounds for anonymous adopt-commit objects

Abstract

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.

Anonymous Agreement: The Janus Algorithm

“…The following theorem proves that the step complexity of Janus is O(n), which is optimal [4], and that its write complexity equals to O( √ n).…”

“…As in the case of anonymous systems, the algorithm relies on a failure detector of the class AΩ and the set of values that can be proposed is unbounded. The algorithm is built in a modular way from several copies of the Janus algorithm and an efficient implementation of m-valued adopt-commit objects due to Aspnes and Ellen [4].…”

“…, c}. Each adopt-commit object is thus implemented by the optimal algorithm by Aspnes and Ellen [4]. A process executing solo, and elected leader by the failure detector from the beginning of the execution, decides after participating in one instance of Janus, and performing one propose() operation on an adopt-commit object.…”

“…Recently, several papers [4,5,13,21,23,28] have addressed the question of the computational power of anonymous systems, with an emphasis on the consensus problem. In particular, Aspnes and Ellen [4] have shown that, when the number of proposed values is unbounded, the solo step complexity of consensus is Θ(n) in an n-process system.…”

“…In particular, Aspnes and Ellen [4] have shown that, when the number of proposed values is unbounded, the solo step complexity of consensus is Θ(n) in an n-process system. This paper presents a new, efficient, consensus algorithm for anonymous system.…”