Efficient Randomized Test-And-Set Implementations
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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(^∗ k) in the location-oblivious adversary model, and the second has expected max-step complexity O( k) against any read/write-oblivious adversary, where k≤ n is the contention. These algorithms improve the previous upper bound by Alistarh and Aspnes [2] of O( n) expected max-step complexity in the oblivious adversary model. We also propose a modification to a TAS algorithm by Alistarh, Attiya, Gilbert, Giurgiu, and Guerraoui [5] for the strong adaptive adversary, which improves its space complexity from super-linear to linear, while maintaining its O( 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( 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 [7] on a similar problem for n≥ 3 processes.
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