The space complexity of long-lived and one-shot timestamp implementations

Helmi, Maryam; Highám, Lisa; Pacheco, Eduardo; Woelfel, Philipp

doi:10.1145/1993806.1993826

Cited by 8 publications

(2 citation statements)

References 25 publications

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“…This section describes our model of computation and the notation, vocabulary and general techniques used in this paper. Previous work by many researchers (for example [8,11,18,19,23,27]) has collectively developed similar tools that serve to make our description of results and presentation of proofs precise, concise and clear. Much of the terminology presented in this section is borrowed or adapted from this previous research.…”

Section: Preliminariesmentioning

confidence: 99%

Space Bounds for Adaptive Renaming

Helmi

Highám

Woelfel

2014

Lecture Notes in Computer Science

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Abstract. We study the space complexity of implementing long-lived and one-shot adaptive renaming from multi-reader multi-writer registers, in an asynchronous distributed system with n processes. As a result of an f -adaptive renaming algorithm each participating process gets a distinct name in the range {1, . . . , f (k)} provided k processes participate.Let f : {1, . . . , n} → N be a non-decreasing function satisfying f (1) ≤ n − 1 and let d = max{x | f (x) ≤ n − 1}. We show that any non-deterministic solo-terminating long-lived f -adaptive renaming object requires d + 1 registers. This implies a lower bound of n − c registers for long-lived (k + c)-adaptive renaming, which we observe is tight.We also prove a lower bound of ⌊ 2(n−c)c+2 ⌋ registers for implementing any non-deterministic soloterminating one-shot (k + c)-adaptive renaming. We provide two one-shot renaming algorithms: a waitfree algorithm and an obstruction-free algorithm. Each algorithm employs a parameter to depict the tradeoff between space and adaptivity. When these parameters are chosen appropriately, this results in a wait-free one-shot ( 2 )-adaptive renaming algorithm from ⌈ √ n⌉ + 1 registers, and an obstruction-free one-shot f -adaptive renaming algorithm from only min{n, x | f (x) ≥ 2n} + 1 registers. 1 mhelmikh@ucalgary.ca, +1 403 210-9416 2 higham@ucalgary.ca, +1 403 220-7696 3 woelfel@ucalgary.ca, +1 403 220-7259

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Section: Preliminariesmentioning

confidence: 99%

Space Bounds for Adaptive Renaming

Helmi

Highám

Woelfel

2014

Lecture Notes in Computer Science

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“…Covering arguments were first used by Burns and Lynch [4] to prove a space lower bound for mutual exclusion, and essentially all space lower bounds are based on this technique. Examples are space lower bounds for onetime test-and-set objects [30], consensus [8], timestamps [6,9], and the general class of perturbable objects [17] (which includes LL/SC among others). These lower bounds have in common that they do not apply if CAS objects are available as base objects.…”

Section: Introductionmentioning

confidence: 99%

On the Time and Space Complexity of ABA Prevention and Detection

Aghazadeh

Woelfel

2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

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We investigate the time and space complexity of detecting and preventing ABAs in shared memory algorithms for systems with n processes and bounded base objects. To that end, we define ABA-detecting registers, which are similar to normal read/write registers, except that they allow a process q to detect with a read operation, whether some process wrote the register since q's last read. ABA-detecting registers can be implemented trivially from a single unbounded register, but we show that they have a high complexity if base objects are bounded: An obstruction-free implementation of an ABA-detecting single bit register cannot be implemented from fewer than n − 1 bounded registers. Moreover, bounded CAS objects (or more generally, conditional read-modify-write primitives) offer little help to implement ABA-detecting single bit registers: We prove a linear time-space tradeoff for such implementations. We show that the same time-space tradeoff holds for implementations of single bit LL/SC primitives from bounded writable CAS objects. This proves that the implementations of LL/SC/VL by Anderson and Moir [2] as well as Jayanti and Petrovic [15] are optimal.We complement our lower bounds with tight upper bounds: We give an implementation of ABA-detecting registers from n + 1 bounded registers, which has step complexity O(1). We also show that (bounded) LL/SC/VL can be implemented from a single bounded CAS object and with O(n) step complexity. Both upper bounds are asymptotically optimal with respect to their time-space product.These results give formal evidence that the ABA problem is inherently difficult, that even writable CAS objects do not provide significant benefits over registers for dealing with the ABA problem itself, and that there is no hope of finding a more efficient implementation of LL/SC/VL from bounded CAS objects and registers than the ones from [2,15].

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Linear Space Bootstrap Communication Schemes

Delporte-Gallet¹,

Fauconnier²,

Gafni³

et al. 2013

Distributed Computing and Networking

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International audienceWe consider a system of n processes with ids not a priori known, that are drawn from a large space, potentially unbounded. How can these n processes communicate to solve a task? We show that n a priori allocated Multi-Writer Multi-Reader (MWMR) registers are both needed and sufficient to solve any read-write wait free solvable task. This contrasts with the existing possible solution borrowed from adaptive algorithms that require Θ(n 2) MWMR registers. To obtain these results, the paper shows how the processes can non blocking emulate a system of n Single-Writer Multi-Reader (SWMR) registers on top of n MWMR registers. It is impossible to do such an emulation with n − 1 MWMR registers. Furthermore, we want to solve a sequence of tasks (potentially infinite) that are sequentially dependent (processes need the previous task's outputs in order to proceed to the next task). A non blocking emulation might starve a process forever. By doubling the space complexity, using 2n − 1 rather than just n registers, the computation is wait free rather than non blocking

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The space complexity of long-lived and one-shot timestamp implementations

Cited by 8 publications

References 25 publications

Space Bounds for Adaptive Renaming

Space Bounds for Adaptive Renaming

On the Time and Space Complexity of ABA Prevention and Detection

Linear Space Bootstrap Communication Schemes

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