Randomized two-process wait-free test-and-set

Tromp, John; Vitányi, Paul M. B.

doi:10.1007/s004460200071

Cited by 16 publications

(27 citation statements)

References 42 publications

(58 reference statements)

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“…In this paper, we will use a randomized two-process test-and-set implementation by Tromp and Vitànyi [Tromp and Vitányi 2002] as a basis for our algorithms. Their algorithm ensures the following properties, whose proofs can be found in their paper.…”

Section: Test-and-set and Compare-and-swapmentioning

confidence: 99%

“…Their algorithm ensures the following properties, whose proofs can be found in their paper. The two-process test-and-set implementation of [Tromp and Vitányi 2002] ensures the following properties.…”

Section: Test-and-set and Compare-and-swapmentioning

confidence: 99%

“…Test-and-set. In this section, the test-and-set objects used as comparators are implemented using the algorithm of Tromp and Vitányi [Tromp and Vitányi 2002]; in Section 7, we will assume hardware implementations of test-andset. This distinction is only important when computing the complexity of the construction, and does not affect its correctness.…”

Section: Renaming Using a Sorting Networkmentioning

confidence: 99%

“…Therefore, the renaming network has the same termination guarantees as the two-process test-and-set algorithm we use. In particular, if we use the two-process test-and-set implementation of [Tromp and Vitányi 2002], the network guarantees termination with probability 1. We prove name uniqueness and namespace tightness by ensuring the following claim.…”

Section: Renaming Using a Sorting Networkmentioning

confidence: 99%

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Tight Bounds for Asynchronous Renaming

Alistarh

Aspnes

Censor-Hillel

et al. 2014

J. ACM

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This paper presents the first tight bounds on the time complexity of shared-memory renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace.We first prove an individual lower bound of Ω(k) process steps for deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. The bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic concurrent fetch-and-increment counters, queues and stacks. The proof is based on a new reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement this individual bound with a global lower bound of Ω(k log(k/c)) on the total step complexity of renaming into a namespace of size ck, for any c ≥ 1. This result applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter implementations, that are tight within logarithmic factors.On the algorithmic side, we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm, with expected cost equal to the depth of the sorting network. This gives a tight adaptive renaming algorithm with expected step complexity O(log k), where k is the contention in the current execution. This algorithm is the first to achieve sublinear time, and it is time-optimal as per our randomized lower bound. Finally, we use this renaming protocol to build monotone-consistent counters with logarithmic step complexity and linearizable fetch-and-increment registers with polylogarithmic cost.

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Section: Test-and-set and Compare-and-swapmentioning

confidence: 99%

Section: Test-and-set and Compare-and-swapmentioning

confidence: 99%

Section: Renaming Using a Sorting Networkmentioning

confidence: 99%

Section: Renaming Using a Sorting Networkmentioning

confidence: 99%

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Tight Bounds for Asynchronous Renaming

Alistarh

Aspnes

Censor-Hillel

et al. 2014

J. ACM

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“…Significant progress has been made in understanding the step complexity of randomized leader election [2,3,6,21,30]. In particular, in the oblivious adversary model (where the order in which processes take steps is independent of random decisions made by processes), the most efficient algorithm guarantees that the expected step complexity (i.e., the expected maximum number of steps executed by any process) is O(log * k), where k is the contention [21].…”

Section: Introductionmentioning

confidence: 99%

An $O(\sqrt n)$ Space Bound for Obstruction-Free Leader Election

Giakkoupis

Helmi

Highám

et al. 2013

Lecture Notes in Computer Science

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Abstract. We present a deterministic obstruction-free implementation of leader election from O( √ n) atomic O(log n)-bit registers in the standard asynchronous shared memory system with n processes. We provide also a technique to transform any deterministic obstruction-free algorithm, in which any process can finish if it runs for b steps without interference, into a randomized wait-free algorithm for the oblivious adversary, in which the expected step complexity is polynomial in n and b. This transformation allows us to combine our obstruction-free algorithm with the leader election algorithm by Giakkoupis and Woelfel [21], to obtain a fast randomized leader election (and thus test-and-set) implementation from O( √ n) O(log n)-bit registers, that has expected step complexity O(log * n) against the oblivious adversary. Our algorithm provides the first sub-linear space upper bound for obstruction-free leader election. A lower bound of Ω(log n) has been known since 1989 [29]. Our research is also motivated by the long-standing open problem whether there is an obstruction-free consensus algorithm which uses fewer than n registers.

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Space- and Time-Efficient Long-Lived Test-And-Set Objects

Aghazadeh

Woelfel

2014

Lecture Notes in Computer Science

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Randomized two-process wait-free test-and-set

Cited by 16 publications

References 42 publications

Tight Bounds for Asynchronous Renaming

Tight Bounds for Asynchronous Renaming

An $O(\sqrt n)$ Space Bound for Obstruction-Free Leader Election

Space- and Time-Efficient Long-Lived Test-And-Set Objects

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