Efficient randomized test-and-set implementations

We study randomized test-and-set (TAS) implementations from registers in the asynchronous shared memory model with n processes. We introduce the problem of group election , a natural variant of leader election, and propose a framework for the implementation of TAS objects from group election objects. We then present two group election algorithms, each yielding an efficient TAS implementation. The first implementation has expected max-step complexity O ( log ∗ k ) in the location-oblivious adversary model, and the second has expected max-step complexity O ( log log k ) against any read/write-oblivious adversary, where k ≤ n is the contention. These algorithms improve the previous upper bound by Alistarh and Aspnes (in: Proceedings of the 25th International Symposium on Distributed Computing, 2011 ) of O ( log log n ) expected max-step complexity in the oblivious adversary model. We also propose a modification to a TAS algorithm devised by Alistarh, Attiya, Gilbert, Giurgiu, and Guerraoui (in: Proceedings of the 24th International Symposium on Distributed Computing, DISC 2010 ) for the strong adaptive adversary, which improves its space complexity from super-linear to linear, while maintaining its O ( log n ) expected max-step complexity. We then describe how this algorithm can be combined with any randomized TAS algorithm that has expected max-step complexity T ( n ) in a weaker adversary model, so that the resulting algorithm has O ( log n ) expected max-step complexity against any strong adaptive adversary and O ( T ( n )) in the weaker adversary model. Finally, we prove that for any randomized 2-process TAS algorithm, there exists a schedule determined by an oblivious adversary such that with probability at least 1 / 4 t one of the processes needs at least t steps to finish its TAS operation. This complements a lower bound by Attiya and Censor-Hillel (SIAM J Comput 39(8):3885–3904, 2010 ) on a similar problem for n ≥ 3 processes.