A <i>ϕ</i>-Competitive Algorithm for Scheduling Packets with Deadlines

Veselý, Pavel; Chrobák, Marek; Jeż, Łukasz; Sgall, Jiřį́

doi:10.1137/1.9781611975482.9

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…Once again, the problem is only interesting if packets can have different values. 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), while the lower bounds are 1.25 against the oblivious adversary [8] and 4/3 against the adaptive adversary [15].…”

Section: Further Related Workmentioning

confidence: 99%

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

Antoniadis,

Englert,

Matsakis

et al. 2024

ACM Trans. Algorithms

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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 evicted. 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 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 practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.6918-competitive, establishing the first \((2-\varepsilon)\) upper bound for the competitive ratio of LQD , for a constant \(\varepsilon \gt 0\) .

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Section: Further Related Workmentioning

confidence: 99%

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

Antoniadis,

Englert,

Matsakis

et al. 2024

ACM Trans. Algorithms

View full text Add to dashboard Cite

show abstract

“…Once again, the problem is only interesting if packets can have different values. 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%

“…where we use that a i+1 ≥ a i ≥ σ i q − 1. Using these two observations, we lower bound the sum of the right-hand sides of ( 32), (33) or (34) over all phases by i≥iq  …”

Section: Total Lqd Profit Assigned To a Queuementioning

confidence: 99%

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

Antoniadis,

Englert,

Matsakis

et al. 2020

Preprint

Self Cite

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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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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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A ϕ-Competitive Algorithm for Scheduling Packets with Deadlines

Cited by 5 publications

References 24 publications

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

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

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

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

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