Log-logarithmic protocols for resolving ethernet and semaphore conflicts

Willard, Dan E.

doi:10.1145/800057.808721

Cited by 13 publications

(8 citation statements)

References 11 publications

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“…We believe that on bursty inputs in general, polynomial backoff backs off too slowly, and exponential backoff provides a more aggressive backoff. Batch arrivals have been considered by several authors [9,11,14,16,17,43] with the goal of routing h-relations, involving multiple channels, while we consider a detailed analysis of one channel. The most relevant work is by Gereb-Graus and Tsantilis [9] (see also [18]), who showed that there is a backoff-backon protocol with an optimal O(n) makespan for the Control Tower Problem.…”

Section: Previous Resultsmentioning

confidence: 99%

Adversarial contention resolution for simple channels

Bender

Farach-Colton

et al. 2005

Proceedings of the Seventeenth Annual ACM Symposium on Parallelism in Algorithms and Architectures

104

135

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This paper analyzes the worst-case performance of randomized backoff on simple multiple-access channels. Most previous analysis of backoff has assumed a statistical arrival model.For batched arrivals, in which all n packets arrive at time 0, we show the following tight high-probability bounds. Randomized binary exponential backoff has makespan Θ(n lg n), and more generally, for any constant r, r-exponential backoff has makespan Θ(n log lg r n). Quadratic backoff has makespan Θ((n/ lg n) 3/2 ), and more generally, for r > 1, r-polynomial backoff has makespan Θ((n/ lg n) 1+1/r ). Thus, for batched inputs, both exponential and polynomial backoff are highly sensitive to backoff constants. We exhibit a monotone superpolynomial subexponential backoff algorithm, called loglog-iterated backoff, that achieves makespan Θ(n lg lg n/ lg lg lg n). We provide a matching lower bound showing that this strategy is optimal among all monotone backoff algorithms. Of independent interest is that this lower bound was proved with a delay sequence argument.In the adversarial-queuing model, we present the following stability and instability results for exponential backoff and loglogiterated backoff. Given a (λ, T )-stream, in which at most n = λT packets arrive in any interval of size T , exponential backoff is stable for arrival rates of λ = O(1/ lg n) and unstable for arrival rates of λ = Ω(lg lg n/ lg n); loglog-iterated backoff is stable for arrival rates of λ = O(1/(lg lg n lg n)) and unstable for arrival rates of λ = Ω(1/ lg n). Our instability results show that bursty input is close to being worst-case for exponential backoff and variants and that even small bursts can create instabilities in the channel.

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Section: Previous Resultsmentioning

confidence: 99%

Adversarial contention resolution for simple channels

Bender

Farach-Colton

et al. 2005

Proceedings of the Seventeenth Annual ACM Symposium on Parallelism in Algorithms and Architectures

104

135

View full text Add to dashboard Cite

show abstract

“…Worst-case/adversarial arrivals. More recently, there has been work on adversarial queueing theory, looking at the worst-case performance [1,4,5,13,14,18,22,26,29,59]. A common theme is that dynamic arrivals are hard to cope with.…”

Section: Introductionmentioning

confidence: 99%

“…A common theme is that dynamic arrivals are hard to cope with. When all the packets begin at the same time, efficient protocols are possible [18,19,21,29,30,59]. When packets begin at different times, the problem is harder.…”

Section: Introductionmentioning

confidence: 99%

How to Scale Exponential Backoff: Constant Throughput, Polylog Access Attempts, and Robustness

Bender¹,

Fineman²,

Gilbert³

et al. 2015

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

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Randomized exponential backoff is a widely deployed technique for coordinating access to a shared resource. A good backoff protocol should, arguably, satisfy three natural properties: (i) it should provide constant throughput, wasting as little time as possible; (ii) it should require few failed access attempts, minimizing the amount of wasted effort; and (iii) it should be robust, continuing to work efficiently even if some of the access attempts fail for spurious reasons. Unfortunately, exponential backoff has some well-known limitations in two of these areas: it provides poor (sub-constant) throughput (in the worst case), and is not robust (to adversarial disruption).The goal of this paper is to "fix" exponential backoff by making it scalable, particularly focusing on the case where processes arrive in an on-line, worst-case fashion. We present a relatively simple backoff protocol, Re-Backoff, that has, at its heart, a version of exponential backoff. It guarantees expected constant throughput with dynamic process arrivals and requires only an expected polylogarithmic number of access attempts per process.Re-Backoff is also robust to periods where the shared resource is unavailable for a period of time. If it is unavailable for D time slots, Re-Backoff provides the following guarantees. When the number of packets is a finite n, the average expected number of access attempts for successfully sending a packet is O(log 2 (n + D)). In the infinite case, the average expected number of access attempts for successfully sending a packet is O(log 2 (η + D)) where η is the maximum number of processes that are ever in the system concurrently.

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“…The WNCD model is one of the simplest parallel computation models which have been studied for more than two decades. Some researchers regarded the model as the broadcast communication model [4]- [7], [9], [13], [15]- [17], [19]- [21], [23], [24]. In the WNCD model some important and essential components were investigated such as the sorting problem [3]- [5], [8], [14], [24], maximum finding problem [7], [15] and graph algorithm [21]- [23].…”

Section: Introductionmentioning

confidence: 99%

Generalization of Sorting in Single Hop Wireless Networks

Shiau

Yang

2006

IEICE Transactions on Information and Systems

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The generalized sorting problem is to find the first k largest elements among n input elements and to report them in a sorted order. In this paper, we propose a fast generalized sorting algorithm under the single hop wireless networks model with collision detection (WNCD). The algorithm is based on the maximum finding algorithm and the sorting algorithm. The key point of our algorithm is to use successful broadcasts to build broadcasting layers logically and then to distribute the data elements into those logic layers properly. Thus, the number of broadcast conflicts is reduced. We prove that the average time complexity required for our generalized sorting algorithm is Θ k + log (n − k). When k = 1, our generalized sorting algorithm does the work of finding maximum, and when k = n, it does the work of sorting. Thus, the analysis of our algorithm builds a connection between the two extremely special cases which are maximum finding and sorting.

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Log-logarithmic protocols for resolving ethernet and semaphore conflicts

Cited by 13 publications

References 11 publications

Adversarial contention resolution for simple channels

Adversarial contention resolution for simple channels

How to Scale Exponential Backoff: Constant Throughput, Polylog Access Attempts, and Robustness

Generalization of Sorting in Single Hop Wireless Networks

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