A Universal Randomized Packet Scheduling Algorithm

Jeż, Łukasz

doi:10.1007/s00453-012-9700-0

Cited by 13 publications

(12 citation statements)

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“…Upper and lower bounds of e/(e−1) [6,22] and 4/3 ≈ 1.333 [6], respectively, against an adaptive adversary were shown. For any fixed s, lower bounds are the same with the bounds in the case in which s is general while upper bounds are 1/(1 − (1 − 1 s ) s ) [22] against the both adversaries. A generalization of the bounded delay buffer management problem has been studied, called the weighted item collection problem [7,8,22].…”

Section: Related Resultsmentioning

confidence: 99%

“…The current best upper and lower bounds for this variant are (1 + √ 5)/2 [25,21] and 1.377 [14], respectively. The research on randomized algorithms for the bounded delay buffer management problem has also been conducted extensively [13,5,9,6,19,20,21,22]. In the case in which s is general, the current best upper and lower bounds are e/(e − 1) ≈ 1.582 [5,9,22] and 5/4 = 1.25 [13], respectively, against an oblivious adversary were shown.…”

Section: Related Resultsmentioning

confidence: 99%

“…In the case in which s is general, the current best upper and lower bounds are e/(e − 1) ≈ 1.582 [5,9,22] and 5/4 = 1.25 [13], respectively, against an oblivious adversary were shown. Upper and lower bounds of e/(e−1) [6,22] and 4/3 ≈ 1.333 [6], respectively, against an adaptive adversary were shown. For any fixed s, lower bounds are the same with the bounds in the case in which s is general while upper bounds are 1/(1 − (1 − 1 s ) s ) [22] against the both adversaries.…”

Section: Related Resultsmentioning

confidence: 99%

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An Optimal Algorithm for 2-Bounded Delay Buffer Management with Lookahead

Kobayashi

2019

Lecture Notes in Computer Science

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The bounded delay buffer management problem, which was proposed by Kesselman et al. an online problem focusing on buffer management of a switch supporting Quality of Service (QoS). The problem definition is as follows: Packets arrive to a buffer over time and each packet is specified by the release time, deadline and value. An algorithm can transmit at most one packet from the buffer at each integer time and can gain its value as the profit if transmitting a packet by its deadline after its release time. The objective of this problem is to maximize the gained profit. We say that an instance of the problem is s-bounded if for any packet, an algorithm has at most s chances to transmit it. For any s ≥ 2, Hajek (CISS 2001) showed that the competitive ratio of any deterministic algorithm is at least (1 + √ 5)/2 ≈ 1.619. It is conjectured that there exists an algorithm whose competitive ratio matching this lower bound for any s. However, it has not been shown yet. Then, when s = 2, Böhm et al. (ISAAC 2016) introduced the lookahead ability to an online algorithm, that is the algorithm can gain information about future arriving packets, and showed that the algorithm achieves the competitive ratio of (−1 + √ 13)/2 ≈ 1.303. Also, they showed that the competitive ratio of any deterministic algorithm is at least (1 + √ 17)/4 ≈ 1.281. In this paper, for the 2-bounded model with lookahead, we design an algorithm with a matching competitive ratio of (1 + √ 17)/4.

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Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

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An Optimal Algorithm for 2-Bounded Delay Buffer Management with Lookahead

Kobayashi

2019

Lecture Notes in Computer Science

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“…Any deterministic online algorithm is at least φ ≈ 1.618-competitive [4,15,22,36], and after a sequence of gradual improvements [16,18,29], Veselý, Chrobak, Jeż, and Sgall [34] recently gave a φ-competitive algorithm. The competitive ratio of randomized algorithms is still open, with the best upper bound of e e−1 ≈ 1.582 [8,14,23] (that holds even against the adaptive adversary) and a lower bound of 1.25 against the oblivious adversary [8] and of 4/3 against the adaptive adversary [15].…”

Section: Related Workmentioning

confidence: 99%

Breaking the Barrier of 2 for the Competitiveness of Longest Queue Drop

Antoniadis,

Englert,

Matsakis

et al. 2020

Preprint

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We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably rejected. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets.The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from the back of whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be 2-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of great practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.707-competitive, establishing the first (2 − ε) upper bound for the competitive ratio of LQD, for a constant ε > 0.

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“…The lower bound of φ in [16,10] does not apply to s-uniform instances; in fact, as shown by Chrobak et al [12], for 2-uniform instances ratio ≈ 1.377 is optimal.Randomized online algorithms for PacketScheduling have been studied as well, although the gap between the upper and lower bounds for the competitive ratio remains quite large. The best upper bound is ≈ 1.582 [4,9,7,22], and it applies even to the adaptive adversary model. For the adaptive adversary the best lower bound is ≈ 1.33 [7], while for the oblivious adversary it is 1.25 [10].Kesselman et al [18] originally proposed the problem in the setting with integer bandwidth m ≥ 1, which means that m packets are sent in each step.…”

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confidence: 99%

A ϕ-Competitive Algorithm for Scheduling Packets with Deadlines

Veselý

Chrobák

Jeż

et al. 2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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In the online packet scheduling problem with deadlines (PacketScheduling, for short), the goal is to schedule transmissions of packets that arrive over time in a network switch and need to be sent across a link. Each packet has a deadline, representing its urgency, and a non-negative weight, that represents its priority. Only one packet can be transmitted in any time slot, so, if the system is overloaded, some packets will inevitably miss their deadlines and be dropped. In this scenario, the natural objective is to compute a transmission schedule that maximizes the total weight of packets which are successfully transmitted. The problem is inherently online, with the scheduling decisions made without the knowledge of future packet arrivals. The central problem concerning PacketScheduling, that has been a subject of intensive study since 2001, is to determine the optimal competitive ratio of online algorithms, namely the worst-case ratio between the optimum total weight of a schedule (computed by an offline algorithm) and the weight of a schedule computed by a (deterministic) online algorithm.We solve this open problem by presenting a φ-competitive online algorithm for PacketScheduling (where φ ≈ 1.618 is the golden ratio), matching the previously established lower bound. arXiv:1807.07177v4 [cs.DS] 28 Jun 2019 Past work. The PacketScheduling problem was first introduced independently by Hajek [16] and Kesselman et al. [18], who both gave a proof that the greedy algorithm (that always schedules the heaviest packet) is 2-competitive. Hajek's paper also contained a proof of a lower bound of φ ≈ 1.618 on the competitive ratio. The same lower bound was later discovered independently by Andelman et al. [3,21] and also by Chin et al. [10] in a different, but equivalent setting. Improving over the greedy algorithm, Chrobak et al. [11,12] gave an online algorithm with competitive ratio 1.939. This was subsequently improved to 1.854 by Li et al. [20], and to 1.828 by Englert and Westermann [14], which, prior to the present paper, has been the best upper bound known.Algorithms with ratio φ have been developed for several restricted variants of PacketScheduling. Li et al. [19] (see also [17]) gave a φ-competitive algorithm for the case of agreeable deadlines, which consists of instances where the deadline ordering is the same as the ordering of release times. Another well-studied case is that of s-bounded instances, where each packet's deadline is within at most s steps from its release time. A φ-competitive algorithm for 2-bounded instances was given by Kesselman et al. [18]. This bound was later extended to 3-bounded instances by Chin et al. [9] and to 4-bounded instances by Böhm et al. [8]. The work of Bienkowski et al. [6] provides an upper bound of φ (in a somewhat more general setting) for the case where packet weights increase with respect to deadlines. (It should be noted that the lower bound of φ applies to instances that are 2-bounded, which implies agreeable-deadlines, and have increasing weights.) In s-uniform inst...

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A Universal Randomized Packet Scheduling Algorithm

Cited by 13 publications

References 14 publications

An Optimal Algorithm for 2-Bounded Delay Buffer Management with Lookahead

An Optimal Algorithm for 2-Bounded Delay Buffer Management with Lookahead

Breaking the Barrier of 2 for the Competitiveness of Longest Queue Drop

A ϕ-Competitive Algorithm for Scheduling Packets with Deadlines

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