Fast Randomized Test-and-Set and Renaming

Alistarh, Dan; Attiya, Hagit; Gilbert, Seth; Giurgiu, Andrei; Guerraoui, Rachid

doi:10.1007/978-3-642-15763-9_9

Cited by 38 publications

(72 citation statements)

References 29 publications

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“…It improves exponentially on previous strong renaming solutions, which had worst-case complexity at least linear, e.g. [Alistarh et al 2010]. It also gives an exponential separation between deterministic and randomized renaming algorithms.…”

Section: An Algorithm For Strong Randomized Renamingmentioning

confidence: 81%

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: An Algorithm For Strong Randomized Renamingmentioning

confidence: 81%

Tight Bounds for Asynchronous Renaming

Alistarh

Aspnes

Censor-Hillel

et al. 2014

J. ACM

Self Cite

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“…The expected runtime of their algorithm is O(M log 2 n), where M is the size of the initial name space. In [4] the authors propose an adaptive implementation of test-andset registers with read-write registers. Based on that implementation, they present a randomized loose renaming algorithm which, w.h.p., requires O(k log 4 k/ log 2 (1 + )) steps using a name space of size (1 + ) · k. This result was further improved in [12] where the authors present operations for implementing test-and-set with a step complexity of O(log * k) for contention k. The authors of [13] obtained strong long-lived randomized renaming with amortized step complexity O(n log n).…”

Section: A Related Workmentioning

confidence: 99%

“…Tight renaming: The authors of [4] present a tight renaming algorithm with a total step complexity of O(n log 3 n). In [7] the authors give two new randomized renaming algorithms which work in the presence of an adaptive adversary.…”

Section: A Related Workmentioning

confidence: 99%

“…In recent years renaming gained new popularity and several papers appeared that investigated renaming in the message-passing model ( [1], [2], [3]) and in the shared memory model ( [4], [5], [6], [7], [9]). Assuming the asynchronous shared memory model, the authors of [7] describe a construction based on the AKS network that assigns all names to a tight name space within O(log n) steps per process.…”

Section: Introductionmentioning

confidence: 99%

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Randomized Renaming in Shared Memory Systems

Berenbrink

Brinkmann

Elsässer

et al. 2015

2015 IEEE International Parallel and Distributed Processing Symposium

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Citation for published item:ferenrinkD etr nd frinkmnnD endr¡ e nd ils¤ sserD oert nd priedetzkyD om nd xgelD vrs @PHISA 9ndomized renming in shred memory systemsF9D in PHIS siii PWth snterntionl rllel nd histriuted roessing ymposium @sh PHISAD PS!PW wy PHISD ryderdD sndi Y proeedingsF vos elmitosX siiiD ppF SRPESRWF rllel nd histriuted roessing ymposium @shAF Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract-Renaming is a task in distributed computing where n processes are assigned new names from a name space of size m. The problem is called tight if m = n, and loose if m > n. In recent years renaming came to the fore again and new algorithms were developed. For tight renaming in asynchronous shared memory systems, Alistarh et al. describe a construction based on the AKS network that assigns all names within O(log n) steps per process. They also show that, depending on the size of the name space, loose renaming can be done considerably faster. For m = (1 + ) · n and constant , they achieve a step complexity of O(log log n).In this paper we consider tight as well as loose renaming and introduce randomized algorithms that achieve their tasks with high probability. The model assumed is the asynchronous shared memory model against an adaptive adversary. Our algorithm for loose renaming maps n processes to a name space of size m = (1 + 2/(log n) ) · n = (1 + o(1)) · n performing O( · (log log n)2 ) test-and-set operations. In the case of tight renaming, we present a protocol that assigns n processes to n names with step complexity O(log n), but without the overhead and impracticality of the AKS network. This algorithm utilizes modern hardware features in form of a counting device which is also described in the paper. This device may have the potential to speed up other distributed algorithms as well.

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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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Fast Randomized Test-and-Set and Renaming

Cited by 38 publications

References 29 publications

Tight Bounds for Asynchronous Renaming

Tight Bounds for Asynchronous Renaming

Randomized Renaming in Shared Memory Systems

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

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