Anonymous obstruction-free (n, k)-set agreement with $$n-k+1$$ n - k + 1 atomic read/write registers

Bouzid, Zohir; Raynal, Michel; Sutra, Pierre

doi:10.1007/s00446-017-0301-7

Cited by 25 publications

(20 citation statements)

References 42 publications

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“…last1i ← (cti = n); (4) release(idi); % realizes an implicit broadcast of cti % (5) if (last1i) (6) then for each x ∈ {1, · · · , m} do SM i[x] ← DESA(x) end for % the permutation for pi is: ∀ y ∈ {1, · · · , m}: map i (y) = y % .BIT still contains its initial value 0, ensures that when the last process (say p k ) that entered the second critical section exits it, it knows that all the processes have computed their mapping function, and no process that executes the "repeat" loop of line 16 can exit it.…”

Section: Proof Of the Algorithmmentioning

confidence: 99%

“…Anonymous memory. While the notion of process anonymity has been studied for a long time from an algorithmic and computability point of view, both in message-passing systems (e.g., [2,5,21]) and shared memory systems (e.g., [4,6,11]), the notion of memory anonymity has been introduced only very recently in [20]. (See [18] for an introductory survey on process and memory anonymity).…”

Section: Introductionmentioning

confidence: 99%

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Mutex-Based De-anonymization of an Anonymous Read/Write Memory

et al. 2019

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Anonymous shared memory is a memory in which processes use different names for the same shared read/write register. As an example, a shared register named A by a process p and a shared register named B by another process q can correspond to the very same register X, and similarly for the names B at p and A at q which can correspond to the same register Y = X. Hence, there is a permanent disagreement on the register names among the processes. This new notion of anonymity was recently introduced by G. Taubenfeld (PODC 2017), who presented several memory-anonymous algorithms and impossibility results.This paper introduces a new problem (new to our knowledge), that consists in "desanonymizing" an anonymous shared memory. To this end, it presents an algorithm that, starting with a shared memory made up of m anonymous read/write atomic registers (i.e., there is no a priori agreement on their names), allows each process to compute a local addressing mapping, such that all the processes agree on the names of each register. The proposed construction is based on an underlying deadlockfree mutex algorithm for n ≥ 2 processes (recently proposed in a paper co-authored by some of the authors of this paper), and consequently inherits its necessary and sufficient condition on the size m of the anonymous memory, namely m must belongs to the set M (n) = {m : such that ∀ : 1 < ≤ n : gcd( , m) = 1} \ {1}. This algorithm, which is also symmetric in the sense process identities can only be compared by equality, requires the participation of all the processes; hence it can be part of the system initialization. Last but not least, the proposed algorithm has a first-class noteworthy property, namely, its simplicity.

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Section: Proof Of the Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mutex-Based De-anonymization of an Anonymous Read/Write Memory

et al. 2019

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“…Memory anonymity. While the notion of process anonymity has been studied for a long time from an algorithmic and computability point of view, both in message-passing systems (e.g., [1,4,17]) and shared memory systems (e.g., [3,5,8]), the notion of memory anonymity has been introduced only very recently by [15]. (See also [11] for an introductory survey on process and memory anonymity.…”

Section: Anonymous Memorymentioning

confidence: 99%

Anonymous Read/Write Memory: Leader Election and De-anonymization

Godard

Imbs

Raynal

et al. 2019

Structural Information and Communication Complexity

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Anonymity has mostly been studied in the context where processes have no identity. A new notion of anonymity was recently introduced at PODC 2017, namely, this notion considers that the processes have distinct identities but disagree on the names of the read/write registers that define the shared memory. As an example, a register named A by a process p and a shared register named B by another process q may correspond to the very same register X, while the same name C may correspond to different registers for p and q. Recently, a memory-anonymous deadlock-free mutual exclusion algorithm has been proposed by some of the authors. This article addresses two different problems, namely election and memory de-anonymization. Election consists of electing a single process as a leader that is known by every process. Considering the shared memory as an array of atomic read/write registers SM [1..m], memory de-anonymization consists in providing each process pi with a mapping function map i () such that, for any two processes pi and pj and any integer x ∈ [1..m], map i (x) and map j (x) allow them to address the same register. Let n be the number of processes and α a positive integer. The article presents election and de-anonymization algorithms for m = α n + β registers, where β is equal to 1, n − 1, or belongs to a set denoted M (n) (which characterizes the values for which mutual exclusion can be solved despite anonymity). The de-anonymization algorithms are based on the use of election algorithms. The article also shows that the size of the permanent control information that, due to de-anonymization, a register must save forever, can be reduced to a single bit.

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“…There are algorithms that solve n-consensus using n registers [AH90, BRS15,Zhu15]. This is tight by the recent result of [EGZ18], which shows a lower bound of n registers for binary consensus among n processes and, hence, for n-consensus.…”

Section: Our Resultsmentioning

confidence: 97%

A Complexity-Based Hierarchy for Multiprocessor Synchronization

Ellen

Gelashvili

Shavit

et al. 2016

Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing

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For many years, Herlihy's elegant computability-based Consensus Hierarchy has been our best explanation of the relative power of various types of multiprocessor synchronization objects when used in deterministic algorithms. However, key to this hierarchy is treating synchronization instructions as distinct objects, an approach that is far from the real-world, where multiprocessor programs apply synchronization instructions to collections of arbitrary memory locations. We were surprised to realize that, when considering instructions applied to memory locations, the computability based hierarchy collapses. This leaves open the question of how to better capture the power of various synchronization instructions.In this paper, we provide an approach to answering this question. We present a hierarchy of synchronization instructions, classified by the space complexity necessary to solve consensus in an obstructionfree manner using these instructions. Our hierarchy provides a classification of combinations of known instructions that seems to fit with our intuition of how useful some are in practice, while questioning the effectiveness of others. In particular, we prove an essentially tight characterization of the power of buffered read and write instructions. Interestingly, we show a similar result for multi-location atomic assignments.

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Anonymous obstruction-free (n, k)-set agreement with $$n-k+1$$ n - k + 1 atomic read/write registers

Cited by 25 publications

References 42 publications

Mutex-Based De-anonymization of an Anonymous Read/Write Memory

Mutex-Based De-anonymization of an Anonymous Read/Write Memory

Anonymous Read/Write Memory: Leader Election and De-anonymization

A Complexity-Based Hierarchy for Multiprocessor Synchronization

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