A theory of competitive analysis for distributed algorithms

Ajtai, Miklós; Aspnes, James; Dwork, Cynthia; Waarts, Orli

doi:10.1109/sfcs.1994.365676

Cited by 40 publications

(82 citation statements)

References 36 publications

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“…We conjecture that there exists a tighter analysis, showing that the deterministic To-Do Tree can have the same asymptotic work and tasksexecuted bounds as the randomized To-Do Tree. Although we omit details here, our approach may also be used to analyze other variants of asynchronous task allocation, such as collect [2], in which processes need to aggregate register values, the at-most-once problem [22] and do-most [20], in which only a fraction of the tasks need be performed.…”

Section: Discussionmentioning

confidence: 99%

“…[4], [14], [16], [23], [25], [26]. Asynchronous task allocation is also related to distributed collect [2], in which p processors need to aggregate values from m registers. Both task allocation and collect have been used for solving other fundamental distributed problems, such as dynamic load balancing [18], mutual exclusion [11], atomic snapshots [1], consensus [7], renaming [13], distributed phase clocks [9], and PRAM simulation [21].…”

Section: Introductionmentioning

confidence: 99%

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How to Allocate Tasks Asynchronously

Alistarh

Bender

Gilbert³

et al. 2012

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

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Abstract-Asynchronous task allocation is a fundamental problem in distributed computing in which p asynchronous processes must execute a set of m tasks. Also known as write-all or do-all, this problem been studied extensively, both independently and as a key building block for various distributed algorithms.In this paper, we break new ground on this classic problem: we introduce the To-DoTree concurrent data structure, which improves on the best known randomized and deterministic upper bounds. In the presence of an adaptive adversary, the randomized To-DoTree algorithm has O(m + p log p log 2 m) work complexity. We then show that there exists a deterministic variant of the To-DoTree algorithm with work complexity O(m+p log 5 m log 2 max(m, p)). For all values of m and p, our algorithms are within log factors of the Ω(m + p log p) lower bound for this problem.The key technical ingredient in our results is a new approach for analyzing concurrent executions against a strong adaptive scheduler. This technique allows us to handle the complex dependencies between the processes' coin flips and their scheduling, and to tightly bound the work needed to perform subsets of the tasks.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

How to Allocate Tasks Asynchronously

Alistarh

Bender

Gilbert³

et al. 2012

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

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“…We consider their maximum values to be H = K = p α , for α > β > 1 constant, where we 1 Shared: 2 Register C = (V 0 , V 1 , P ) 3 Vector of MaxArrays MA, with maximum values…”

Section: A An Unbounded Maxarray Implementationmentioning

confidence: 99%

“…[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]. The book by Georgiou and Shvartsman [17] gives a detailed history of the problem.…”

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confidence: 99%

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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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Adaptability and the Usefulness of Hints (Extended Abstract)

Berman

Garay²

1998

Algorithms — ESA’ 98

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In this paper we study the problem of designing algorithms in situations where there is some information concerning the typical conditions that are encountered when the respective problem is solved. The basic goal is to assure efficient performance in the typical case, while satisfying the correctness requirements in every case. We introduce adaptability, a new measure for the quality of an algorithm, which generalizes competitive analysis and related frameworks. This new notion applies to sequential, parallel and distributed algorithms alike. In a nutshell, a "hint" function conveys certain information about the environment in which the algorithm operates. Adaptability compares the performance of the algorithm against the "specialist"-an algorithm specifically tuned to the particular hint value. From this perspective, finding that no single algorithm can adapt to all possible hint values is not necessarily a negative result, provided that a family of specialists can be constructed. Our case studies provide examples of both kinds. We first consider the "ancient" problem of on-line scheduling of jobs in m identical processors, and show that no algorithm can fully adapt to the natural hint of largest job size. In particular, for the cases m = 2, 3, we present specialists that beat the general lower bound for on-line makespan. In the domain of distributed computing, we analyze the Distributed Consensus problem under several hint functions. To fulfill the requirements of one of the cases we consider, we present the first consensus algorithm that is simultaneously optimal in number of processors, early-stopping property (that is, it runs in time proportional to the actual number of faults), and total number of communicated bits. In our new parlance, the algorithm adapts to the number of faults hint with both running time and communication.Work partly done while the author was visiting the Centrum voor Wiskunde en Informatica (CWI), Amsterdam, NL, and at the IBM T.

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A theory of competitive analysis for distributed algorithms

Cited by 40 publications

References 36 publications

How to Allocate Tasks Asynchronously

How to Allocate Tasks Asynchronously

Dynamic Task Allocation in Asynchronous Shared Memory

Adaptability and the Usefulness of Hints (Extended Abstract)

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