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The natural workstealing algorithm is stable
 In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS
, 2001
"... In this paper we analyse a very simple dynamic workstealing algorithm. In the workgeneration model, there are n (work) generators. A generatorallocation function is simply a function from the n generators to the n processors. We consider a fixed, but arbitrary, distribution D over generatoralloca ..."
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Cited by 35 (1 self)
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In this paper we analyse a very simple dynamic workstealing algorithm. In the workgeneration model, there are n (work) generators. A generatorallocation function is simply a function from the n generators to the n processors. We consider a fixed, but arbitrary, distribution D over generatorallocation functions. During each timestep of our process, a generatorallocation function h is chosen from D, and the generators are allocated to the processors according to h. Each generator may then generate a unittime task which it inserts into the queue of its host processor. It generates such a task independently with probability λ. After the new tasks are generated, each processor removes one task from its queue and services it. For many choices of D, the workgeneration model allows the load to become arbitrarily imbalanced, even when λ < 1. For example, D could be the point distribution containing a single function h which allocates all of the generators to just one processor. For this choice of D, the chosen processor receives around λn units of work at each step and services one. The natural workstealing algorithm that we analyse is widely used in practical applications and works as follows. During each time step, each empty
Allocating Weighted Jobs in Parallel
, 1997
"... It is well known that after placing m n balls independently and uniformly at random (i.u.r.) into n bins, the fullest bin contains \Theta(log n= log log n+ m n ) balls, with high probability. It is also known (see [Ste96]) that a maximum load of O \Gamma m n \Delta can be obtained for all m n ..."
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Cited by 16 (4 self)
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It is well known that after placing m n balls independently and uniformly at random (i.u.r.) into n bins, the fullest bin contains \Theta(log n= log log n+ m n ) balls, with high probability. It is also known (see [Ste96]) that a maximum load of O \Gamma m n \Delta can be obtained for all m n if a ball is allocated in one (suitably chosen) of two (i.u.r.) bins. Stemann ([Ste96]) shows that r communication rounds suffice to guarantee a maximum load of maxf r p log n; O \Gamma m n \Delta g, with high probability. Adler et al. have shown in [ACMR95] that Stemanns protocol is optimal for constant r. In this paper we extend the above results in two directions: We generalize the lower bound to arbitrary r log log n. This implies that the result of Stemanns protocol is optimal for all r. Our main result is a generalization of Stemanns upper bound to weighted jobs: Let W A (W M ) denote the average (maximum) weight of the balls. Further let \Delta = W A =W M . Note that...
Design of the PRESTO Multimedia Storage Network
, 1999
"... In this paper, we present concepts and simulation results for the design of the Paderborn realtime storage network, short PRESTO, which is currently developed at the Paderborn University in a joint project of the Electrical Engineering Department and the Computer Science Department. In this proj ..."
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In this paper, we present concepts and simulation results for the design of the Paderborn realtime storage network, short PRESTO, which is currently developed at the Paderborn University in a joint project of the Electrical Engineering Department and the Computer Science Department. In this project, we aim at constructing a scalable and faulttolerant storage network that manages a set of parallel disks in a resource ecient way and that can support the realtime delivery of data. We discuss in this paper the principal concepts of the PRESTO storage network, concentrating on data placement and load balancing strategies. Furthermore, we present simulation results that demonstrate that our techniques achieve a high disk utilization together with a low latency with a very high degree of reliability.
unknown title
, 2015
"... 1 The power of two random choices We will now show that two random choices can reduce the maximum load to O(ln lnn). The proof technique is due to Azar et al. [ABKU94, ABKU99] and various applications were explored by Mitzenmacher in his thesis [Mit96]. We first provide the intuition for the proof. ..."
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1 The power of two random choices We will now show that two random choices can reduce the maximum load to O(ln lnn). The proof technique is due to Azar et al. [ABKU94, ABKU99] and various applications were explored by Mitzenmacher in his thesis [Mit96]. We first provide the intuition for the proof. For each i, let Bi denote the number of bins with at least i balls. Suppose Bi ≤ βi for some bound βi. Then Bi+1 is bounded above by a binomial random variable corresponding to the number of heads in n independent coin tosses, where the probability of each toss being heads is at most (βi/n) 2. This is because for a ball to land a bin such that the load of the bin becomes greater than i, it must happen that both the random bins which we chose to put it in, had load at least i. This happens with probability at most (βi/n) 2. Thus, Bi+1 is upper bounded by the above random variable, which we denote as Bin n, βi
The Natural WorkStealing Algorithm is Stable
, 2001
"... Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or othe ..."
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Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available. Copies of full items can be used for personal research or study, educational, or notforprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions: The version presented in WRAP is the published version or, version of record, and may be cited as it appears here.For more information, please contact the WRAP Team at:
Allocating Independent Tasks
, 1997
"... One of the most important problems in the efficient use of parallel systems is to distribute the workload evenly among the servers. An instance of this problem is the problem of independent allocations where the tasks can be executed independently. This paper presents an overview on some results obt ..."
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One of the most important problems in the efficient use of parallel systems is to distribute the workload evenly among the servers. An instance of this problem is the problem of independent allocations where the tasks can be executed independently. This paper presents an overview on some results obtained by several authors for the independent allocation problem using an approach of Azar, Broder, Karlin, and Upfal. The algorithms presented here apply to several problems, including LoadBalancing in distributed computing, choosing Internet connections, scheduling requests on Video on Demand Servers, and Hashing. The allocation problem is known to be NPComplete. Our focus in this paper is on randomized algorithm obtaining feasible solutions very fast; all algorithms presented have sublogarithmic running time. Most algorithms show a tradeoff between time used for communication and quality of solution. Additionally we present lower bounds for the allocation problem. The lower bounds show ...
Continuous and Parallel Allocation of Weighted Jobs
, 1999
"... In recent years the task of allocating jobs to servers has been studied with the \balls and bins" abstraction. Results in this area exploit the large decrease in maximum load that can be achieved by allowing each job (ball) a very small amount of choice in choosing its destination server (bi ..."
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In recent years the task of allocating jobs to servers has been studied with the \balls and bins" abstraction. Results in this area exploit the large decrease in maximum load that can be achieved by allowing each job (ball) a very small amount of choice in choosing its destination server (bin). In this paper, we present such an algorithm for allocating jobs arriving in parallel over an innite time line. In more detail, we assume that in each on an unbounded number of rounds a large batch of jobs arrives at the system that has to be allocated concurrently. Each ball comes with a weight W i 1 that e.g. can model the required runtime of the task represented by the ball. We show that our simple allocation algorithm results in a maximum waiting time of log log n rounds. To achieve this result, we apply the general framework that is represented in [BMS98]. The technique reduces the proof that w.h.p. there exists no bin with a certain load in the case of weighted balls, to the p...