Performing tasks on synchronous restartable message-passing processors

Chlebus, Bogdan S.; Prisco, Roberto De; Shvartsman, Alexander A.

doi:10.1007/pl00008926

Cited by 40 publications

(26 citation statements)

References 15 publications

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“…The Do-All problem was introduced by Dwork et al [1], and investigated in a number of papers [6][7][8][9][10]. All the previous papers considered message-passing models, in which every node can send a message to any subset of nodes in one round.…”

Section: Previous Workmentioning

confidence: 99%

“…That paper also proposed effort as a measure of efficiency, which is work and communication combined. The earlier work [1,6,9,10] concentrated on the adversary who could fail all the stations but one. Some recent work [7,8] concerned optimizing solutions against weaker adversaries.…”

Section: Previous Workmentioning

confidence: 99%

“…This was achieved as a by-product of their investigation of the Byzantine agreement with stop-failures, for which they found a messageoptimal solution. Chlebus et al [6] studied failure models allowing restarts. Restarted processors could contribute to the task-oriented work, but the cost of integrating them into the system, in terms of the available processor steps and communication, might well surpass the benefits.…”

Section: Previous Workmentioning

confidence: 99%

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Performing work in broadcast networks

2005

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We consider the problem of how to schedule t similar and independent tasks to be performed in a synchronous distributed system of p stations communicating via multiple-access channels. Stations are prone to crashes whose patterns of occurrence are specified by adversarial models. Work, defined as the number of the available processor steps, is the complexity measure. We consider only reliable algorithms that perform all the tasks as long as at least one station remains operational. It is shown that every reliable algorithm has to perform work (t + p √ t) even when no failures occur. An optimal deterministic algorithm for the channel with collision detection is developed, which performs work O(t + p √ t). Another algorithm, for the channel without collision detection, performs work O(t + p √ t + p min{ f, t}), where f < p is the number of failures. This algorithm is proved to be optimal, provided that the adversary is restricted in failing no more than f stations. Finally, we consider the question if randomization helps against weaker adversaries for the channel without collision detection. A randomized algorithm is developed which performs the expected minimum amount O(t + p √ t) of work, provided that the adversary may fail a constant fraction of stations and it has to select failure-prone stations prior to the start of an execution of the algorithm.

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Section: Previous Workmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

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Performing work in broadcast networks

2005

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“…For these two schemes, see Kulkarni et al [14], [15]. Further models and methods of failure recovery are in Chlebus et al [9] for restartable processors and in De Prisco et al [10] (stage checkpointing)…”

Section: Introductionmentioning

confidence: 99%

Markov Renewal Methods in Restart Problems in Complex Systems

Asmussen

Lipsky

Thompson

2015

The Fascination of Probability, Statistics and Their Applications

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A task with ideal execution time L such as the execution of a computer program or the transmission of a file on a data link may fail, and the task then needs to be restarted. The task is handled by a complex system with features similar to the ones in classical reliability: failures may be mitigated by using server redundancy in parallel or k-out-of-n arrangements, standbys may be cold or warm, one or more repairmen may take care of failed components, etc. The total task time X (including restarts and pauses in failed states) is investigated with particular emphasis on the tail P(X > x). A general alternating Markov renewal model is proposed and an asymptotic exponential form P(X > x) ∼ Ce −γx identified for the case of a deterministic task time L ≡ . The rate γ is given by equating the spectral radius of a certain matrix to 1, and the asymptotic form of γ = γ( ) as → ∞ is derived, leading to the asymptotics of P(X > x) for random task times L. A main finding is that X is always heavy-tailed if L has unbounded support. The case where the Markov renewal model is derived by lumping in a continuous-time finite Markov process with exponential holding times is given special attention, and the study includes analysis of the effect of processing rates that differ with state or time.

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“…[4,5,[11][12][13]16,19,[22][23][24], has focused on algorithms and lower bounds for the asynchronous version of task allocation, also known as do-all [17], or write-all [19], where processes move at arbitrary speeds and are crash-prone. Task allocation is closely connected to many other fundamental distributed problems, such as mutual exclusion [10], distributed clocks [8], and shared-memory collect [3].…”

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confidence: 99%

Dynamic Task Allocation in Asynchronous Shared Memory

Alistarh¹,

Aspnes²,

Bender³

et al. 2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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Task allocation is a classic distributed problem in which a set of p potentially faulty processes must cooperate to perform a set of tasks. This paper considers a new dynamic version of the problem, in which tasks are injected adversarially during an asynchronous execution. We give the first asynchronous shared-memory algorithm for dynamic task allocation, and we prove that our solution is optimal within logarithmic factors. The main algorithmic idea is a randomized concurrent data structure called a dynamic to-do tree, which allows processes to pick new tasks to perform at random from the set of available tasks, and to insert tasks at random empty locations in the data structure. Our analysis shows that these properties avoid duplicating work unnecessarily. On the other hand, since the adversary controls the input as well the scheduling, it can induce executions where lots of processes contend for a few available tasks, which is inefficient. However, we prove that every algorithm has the same problem: given an arbitrary input, if OPT is the worst-case complexity of the optimal algorithm on that input, then the expected work complexity of our algorithm on the same input is O(OPT log 3 m), where m is an upper bound on the number of tasks that are present in the system at any given time.

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Performing tasks on synchronous restartable message-passing processors

Cited by 40 publications

References 15 publications

Performing work in broadcast networks

Performing work in broadcast networks

Markov Renewal Methods in Restart Problems in Complex Systems

Dynamic Task Allocation in Asynchronous Shared Memory

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