Test-and-Set in Optimal Space

Giakkoupis, George; Helmi, Maryam; Highám, Lisa; Woelfel, Philipp

doi:10.1145/2746539.2746627

Cited by 8 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Space Reference Comments strong adaptive unbounded ⌈log n⌉ + 1 [21] deadlock-free only strong adaptive O(1) Θ(1) [22,23] 2-process implementation strong adaptive O(log n) Θ(n) [1] strong adaptive O(log k) Θ(n 3 ) [5] k is the contention r/w-oblivious O(log log n) Θ(n 3 ) [2] location-oblivious O(log * k) Θ(n) Theorem 4r/w-oblivious O(log log k) Θ(n) Theorem 6strong adaptive O(log k) Θ(n) Theorem 7oblivious O(log * k) Θ(log n) [13] uses impl. of Theorem 4 Table 1: Randomized TAS implementations.…”

Section: Adversary Timementioning

confidence: 99%

“…Until recently, it was not unknown whether any randomized wait-free (or obstruction-free) TAS implementation exists that uses fewer than O(n) registers. After completion of the draft of this paper, Giakkoupis, Helmi, Higham, and Woelfel [12,13] presented deterministic obstruction-free algorithms that use only O( √ n) and O(log n) registers, respectively. As the authors observed, these algorithms can be turned into randomize wait-free ones, and can be combined with the first algorithm proposed in this paper to achieve O(log * n) expected max-step complexity in the oblivious adversary model, with O( √ n) and O(log n) space complexity, respectively.…”

Section: Adversary Timementioning

confidence: 99%

“…It is similar to the AA-algorithm, but introduces a new idea that makes it adaptive. Θ(log n) [13] uses impl. of Theorem 4…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient randomized test-and-set implementations

Giakkoupis

Woelfel

2019

Distrib. Comput.

Self Cite

View full text Add to dashboard Cite

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 [2] of O(log log 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 superlinear 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 [7] on a similar problem for n ≥ 3 processes.can lose. I.e., if all participating processes finish the protocol, then exactly one of them returns win and all others return lose. Obviously, any TAS object immediately yields a leader election protocol: Each process executes a single TAS() operation and returns win if the TAS() call returns 0, or lose if TAS() returns 1. Similarly, a leader election algorithm, together with one additional register, can be used to implement a linearizable TAS object with just a constant increase in the number of steps [15]. Similar transformations from leader election to linearizable TAS objects are implicit in several TAS algorithms, e.g., [1,2].Early randomized TAS implementations assumed a strong adaptive adversary model, where the adversary bases its scheduling decisions on the entire past history of events, including the coin flips by processes. Tromp, and Vitányi [22,23] presented a randomized implementation for two processes which has constant expected max-step complexity and constant space complexity against any strong adaptive adversary. (The max-step complexity of an execution is the maximum number of steps any process needs to finish its algorithm in the execution. See Section 2.2 for formal definitions and a discussion.) Afek, Gafni, Tromp, and Vitányi [1] gave a deterministic implementation of a TAS object for n processes,...

show abstract

Section: Adversary Timementioning

confidence: 99%

Section: Adversary Timementioning

confidence: 99%

See 1 more Smart Citation

Efficient randomized test-and-set implementations

Giakkoupis

Woelfel

2019

Distrib. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another related line of work has focused on the space complexity of this problem, which is now resolved. Specifically, it is known that Ω(log n) distinct registers are necessary [28,16], and a breakthrough result by Giakkoupis, Helmi, Higham, and Woelfel [15] provided the first asymptotically matching upper bound of O(log n), improving upon an O( √ n) algorithm by the same authors [14]. The clear gap in the complexity landscape for this problem concerns time complexity lower bounds.…”

Section: Introductionmentioning

confidence: 99%

Lower Bounds for Shared-Memory Leader Election under Bounded Write Contention

Alistarh¹,

Gelashvili²,

Nadiradze³

2021

Preprint

View full text Add to dashboard Cite

This paper gives tight logarithmic lower bounds on the solo step complexity of leader election in an asynchronous shared-memory model with single-writer multi-reader (SWMR) registers, for both deterministic and randomized obstruction-free algorithms. The approach extends to lower bounds for deterministic and randomized obstruction-free algorithms using multi-writer registers under bounded write concurrency, showing a trade-off between the solo step complexity of a leader election algorithm, and the worst-case number of stalls incurred by a processor in an execution.

show abstract

“…On the other hand, an O( √ n) deterministic obstruction-free upper bound was given in [GHHW13]. The final breakthrough was the recent obstruction-free algorithm designed by Giakkoupis et al [GHHW14], with O(log n) space complexity, essentially closing the problem 1 . For consensus, an upper bound with n registers was long known from [AH90].…”

Section: Introductionmentioning

confidence: 99%

On the optimal space complexity of consensus for anonymous processes

Gelashvili¹

2018

Distrib. Comput.

View full text Add to dashboard Cite

The optimal space complexity of consensus in shared memory is a decades-old open problem. For a system of n processes, no algorithm is known that uses a sublinear number of registers. However, the best known lower bound due to Fich, Herlihy, and Shavit requires Ω( √ n) registers. The special symmetric case of the problem where processes are anonymous (run the same algorithm) has also attracted attention. Even in this case, the best lower and upper bounds are still Ω( √ n) and O(n). Moreover, Fich, Herlihy, and Shavit first proved their lower bound for anonymous processes, and then extended it to the general case. As such, resolving the anonymous case might be a significant step towards understanding and solving the general problem.In this work, we show that in a system of anonymous processes, any consensus algorithm satisfying nondeterministic solo termination has to use Ω(n) read-write registers in some execution. This implies an Ω(n) lower bound on the space complexity of deterministic obstruction-free and randomized wait-free consensus, matching the upper bound and closing the symmetric case of the open problem. 1 The space complexity of randomized test-and-set against a strong (adaptive) adversary remains open.

show abstract

Test-and-Set in Optimal Space

Cited by 8 publications

References 25 publications

Efficient randomized test-and-set implementations

Efficient randomized test-and-set implementations

Lower Bounds for Shared-Memory Leader Election under Bounded Write Contention

On the optimal space complexity of consensus for anonymous processes

Contact Info

Product

Resources

About