Collecting Weighted Items from a Dynamic Queue

Bieńkowski, Marcin; Chrobák, Marek; Dürr, Christoph; Hurand, Mathilde; Jeż, Artur; Jeź, źUkasz; Stachowiak, Grzegorz

doi:10.1007/s00453-011-9574-6

Cited by 12 publications

(15 citation statements)

References 12 publications

(19 reference statements)

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“…As we mentioned before, REMIX is optimal among randomized memoryless algorithms for Item Collection [3,Theorem 7]. In fact, as noted therein, the lower bound proof gives an infinite sequence of adversary's strategies parametrized by N such that the N -th one forces ratio 1/(1 − (1 − 1 N ) N ), while ensuring that the number of packets pending for the algorithm never exceeds N .…”

Section: Optimality For Item Collectionmentioning

confidence: 95%

“…The following generalization of Packet Scheduling has been studied [3], and called Item Collection by its authors. In Item Collection the algorithm is to collect weighted items, one per step, from a dynamic queue S, which is in fact an ordered list.…”

Section: Generalization: Collecting Weighted Items From a Dynamic Queuementioning

confidence: 99%

“…While the paper of Bienkowski's et al [3] focuses on deterministic algorithms for Item Collection, it does provide a lower bound for memoryless randomized algorithms, matched by REMIX, cf. Sect.…”

Section: Generalization: Collecting Weighted Items From a Dynamic Queuementioning

confidence: 99%

See 2 more Smart Citations

A Universal Randomized Packet Scheduling Algorithm

Jeż

2012

Algorithmica

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We give a memoryless scale-invariant randomized algorithm REMIX for Packet Scheduling that is e/(e − 1)-competitive against an adaptive adversary. REMIX unifies most of previously known randomized algorithms, and its general analysis yields improved performance guarantees for several restricted variants, including the s-bounded instances. In particular, REMIX attains the optimum competitive ratio of 4/3 on 2-bounded instances.Our results are applicable to a more general problem, called Item Collection, in which only the relative order between packets' deadlines is known. REMIX is the optimal memoryless randomized algorithm against adaptive adversary for that problem.

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Section: Optimality For Item Collectionmentioning

confidence: 95%

Section: Generalization: Collecting Weighted Items From a Dynamic Queuementioning

confidence: 99%

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A Universal Randomized Packet Scheduling Algorithm

Jeż

2012

Algorithmica

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“…Focusing on the randomized setting, the best online algorithm attains a ratio of 1 − 1/e ≈ 0.632 [6,8], while it is known that no online algorithm can attain a ratio better than 0.8 [9]. Several additional papers addressing the bounded delay model or its variants are [27,10,7]. Kesselman et al [21] also initiated the study of the FIFO-queue model.…”

Section: Related Workmentioning

confidence: 96%

Buffer management for colored packets with deadlines

Azar

Feige

Gamzu

et al. 2009

Proceedings of the Twenty-First Annual Symposium on Parallelism in Algorithms and Architectures

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We consider buffer management of unit packets with deadlines for a multi-port device with reconfiguration overhead. The goal is to maximize the throughput of the device, i.e., the number of packets delivered by their deadline. For a single port or with free reconfiguration, the problem reduces to the well-known packets scheduling problem, where the celebrated earliest-deadline-first (EDF) strategy is optimal 1-competitive. However, EDF is not 1-competitive when there is a reconfiguration overhead. We design an online algorithm that achieves a competitive ratio of 1 − o(1) when the ratio between the minimum laxity of the packets and the number of ports tends to infinity. This is one of the rare cases where one can design an almost 1-competitive algorithm. One ingredient of our analysis, which may be interesting on its own right, is a perturbation theorem on EDF for the classical packets scheduling problem. Specifically, we show that a small perturbation in the release and deadline times cannot significantly degrade the optimal throughput. This implies

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“…Turning to the randomized setting, the best online algorithm attains a ratio of e/(e − 1) [9,12], while no randomized online algorithm can attain a ratio better than 1.25 [13]. Some additional papers studying this model and other variants are [3,8,24,1,25,29,36,17,14,19,10].…”

Section: Related Workmentioning

confidence: 98%

The loss of serving in the dark

Azar

Cohen

Gamzu

2013

Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing

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We study the following balls and bins stochastic process: There is a buffer with B bins, and there is a stream of balls X = X1, X2, . . . , XT such that Xi is the number of balls that arrive before time i but after time i − 1. Once a ball arrives, it is stored in one of the unoccupied bins. If all the bins are occupied then the ball is thrown away. In each time step, we select a bin uniformly at random, clear it, and gain its content. Once the stream of balls ends, all the remaining balls in the buffer are cleared and added to our gain. We are interested in analyzing the expected gain of this randomized process with respect to that of an optimal gain-maximizing strategy, which gets the same online stream of balls, and clears a ball from a bin, if exists, at any step. We name this gain ratio the loss of serving in the dark.In this paper, we determine the exact loss of serving in the dark. We prove that the expected gain of the randomized process is worse by a factor of ρ + from that of the optimal gain-maximizing strategy for any > 0, where ρ = maxα>1 αe α /((α − 1)e α + e − 1) ≈ 1.69996 and B = Ω(1/ 3 ). We also demonstrate that this bound is essentially tight as there are specific ball streams for which the above-mentioned gain ratio tends to ρ. Our stochastic process occurs naturally in many applications. We present a prompt and truthful mechanism for bounded capacity auctions, and an application relating to packets scheduling..

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Collecting Weighted Items from a Dynamic Queue

Cited by 12 publications

References 12 publications

A Universal Randomized Packet Scheduling Algorithm

A Universal Randomized Packet Scheduling Algorithm

Buffer management for colored packets with deadlines

The loss of serving in the dark

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