Tight bounds for k-set agreement with limited-scope failure detectors

Herlihy, Maurice; Penso, Lúcia Draque

doi:10.1007/s00446-005-0141-8

Cited by 27 publications

(26 citation statements)

References 17 publications

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“…This protocol assumes t < k + x − 1 (which means that (t + 1) − (x − 1) is the smallest value of k that it can tolerate). Using topological methods, it has been shown in [27] that this is actually a lower bound for any S x -based k-set agreement protocol (from which it follows that the previous protocol is optimal with respect to the number of faulty processes that can be tolerated). When the limited scope accuracy property has to hold only after some unknown but finite time, we get the class denoted 3S x .…”

Section: Related Workmentioning

confidence: 97%

The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement

Mostéfaoui¹,

Rajsbaum²,

Raynal³

et al. 2008

SIAM J. Comput.

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Abstract:To cope with the impossibility of solving agreement problems in asynchronous systems made up of n processes and prone to t process crashes, system designers tailor their algorithms to run fast in "normal" circumstances. Two orthogonal notions of "normality" have been studied in the past through failure detectors that give processes information about process crashes, and through conditions that restrict the inputs to an agreement problem. This paper investigates how the two approaches can benefit from each other to solve the k-set agreement problem, where processes must agree on at most k of their input values (when k = 1 we have the famous consensus problem). It proposes novel failure detectors for solving k-set agreement, and a protocol that combines them with conditions, establishing a new bridge among asynchronous, synchronous and partially synchronous systems with respect to agreement problems. The paper proves also a lower bound when solving the k-set agreement problem with a condition. Key-words:

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Section: Related Workmentioning

confidence: 97%

The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement

Mostéfaoui¹,

Rajsbaum²,

Raynal³

et al. 2008

SIAM J. Comput.

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“…Informally, a failure detector of the class 3S x is for a system made up of a single cluster of processes; it states that there is a correct process that is eventually never erroneously suspected by any process in that cluster. The technical report [33] describes the extension to q disjoint clusters and the circumstances under which k-set agreement can be solved in this model, which were proved first in [22].…”

Section: S Rajsbaum M Raynal C Traversmentioning

confidence: 99%

“…Then, using a simple topological observation, it is easy to derive the lower bound of [22] for solving k-set agreement in a system enriched with C. In the approach presented in this paper, the technically difficult proofs are encapsulated in algorithmic reductions between the shared memory model and the IRIS model, while in the proof of [22] combinatorial topology techniques introduced in [23] are used to derive the topological properties of the runs of the system enriched with C directly.…”

Section: S Rajsbaum M Raynal C Traversmentioning

confidence: 99%

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The Iterated Restricted Immediate Snapshot Model

Rajsbaum¹,

Raynal

Travers

Lecture Notes in Computer Science

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Abstract:In the Iterated Immediate Snapshot model (IIS ) the memory consists of a sequence of one-shot Immediate Snapshot (IS ) objects. Each IS object can be accessed with an operation that atomically writes a value and returns a snapshot of its contents. Each process can access each IS object at most once. Processes access the sequence of IS objects, one-by-one, asynchronously, in a wait-free manner; any number of processes can crash. It has been shown by Borowsky and Gafni and others that this model is very useful to study the usual read/write shared memory model. Its interest lies in the elegant recursive structure of its runs, hence of the ease to analyze it round by round. In a very interesting way, Borowsky and Gafni have shown that the IIS model and the read/write model are equivalent for the wait-free solvability of decision tasks.In this paper we extend the benefits of the IIS model to partially synchronous systems. Given a shared memory model enriched with a failure detector, what is an equivalent IIS model? The paper shows that an elegant way of capturing the power of a failure detector and other partially synchronous systems in the IIS model is by restricting appropriately its set of runs, giving rise to the Iterated Restricted Immediate Snapshot model (IRIS ).The benefit of the proposed approach is new results (including new proofs of existing results) when we consider the IRIS model instead of the equivalent read/write model enriched with a given failure detector directly. As a study case, the paper considers a system enriched with limited-scope accuracy failure detectors, where there is a cluster of processes such that eventually some correct process is eventually never suspected by any process in that cluster. The paper provides a new proof of the k-set agreement Herlihy and Penso's lower bound for shared memory system augmented with a limited-scope accuracy failure detector. The proof is based on an extension of the Borowsky-Gafni IIS simulation to encompass failure detectors, followed by a very simple topological argumentation.With the IRIS model we have succeeded in capturing the partial synchrony of a failure detector enriched system via a fully asynchronous, round by round system. We thus hope to have contributed to a better understanding of fault-tolerant distributed computing. Key-words:Algorithmic reduction, Asynchronous system, Distributed algorithm, Distributed Computability, Failure detectors, Fault-tolerance, Round-based computation, Shared memory, Topology. IntroductionA distributed model of computation consists of a set of n processes communicating through some medium (some form of message passing or shared memory), satisfying specific timing assumptions (process speeds and communication delays), and failure assumptions (their number and severity). A major obstacle in the development of a theory of distributed computing is the wide variety of models that can be defined -many of which represent real systems -with combinations of parameters in both the (a)synchrony and failure dimen...

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“…While k-set agreement can be easily solved in asynchronous systems where the number t of processes that crash is < k (each of a set of k predetermined processes broadcasts its value, and a process decides the first value it receives), this problem has no solution when k t [1,11,19]. The failure detector approach to solve the k-set agreement problem in message-passing systems has been investigated in [10,14,15,20].…”

Section: Introductionmentioning

confidence: 99%

In Search of the Holy Grail: Looking for the Weakest Failure Detector for Wait-Free Set Agreement

Raynal

Travers

2006

Lecture Notes in Computer Science

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Asynchronous failure detector-based set agreement algorithms proposed so far assume that all the processes participate in the algorithm. This means that (at least) the processes that do not crash propose a value and consequently execute the algorithm. It follows that these algorithms can block forever (preventing the correct processes from terminating) when there are correct processes that do not participate in the algorithm. This paper investigates the wait-free set agreement problem, i.e., the case where the correct participating processes have to decide a value whatever the behavior of the other processes (i.e., the processes that crash and the processes that are correct but do not participate in the algorithm). The paper presents a wait-free set agreement algorithm. This algorithm is based on a leader failure detector class that takes into account the notion of participating processes. Interestingly, this algorithm enjoys a first class property, namely, design simplicity. Key-words:Asynchronous algorithm, Asynchronous system, Atomic register, Consensus, Leader oracle, Participating process, Set agreement, Shared object, Wait-free algorithm.

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Tight bounds for k-set agreement with limited-scope failure detectors

Cited by 27 publications

References 17 publications

The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement

The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement

The Iterated Restricted Immediate Snapshot Model

In Search of the Holy Grail: Looking for the Weakest Failure Detector for Wait-Free Set Agreement

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