The zero-one principle for switching networks

We study the problem of online packet routing and information gathering in lines, rings and trees. A network consists of n nodes. At each node there is a buffer of size B. Each buffer can transmit one packet to the next buffer at each time step. The packets injection is under adversarial control. Packets arriving at a full buffer must be discarded. In information gathering all packets have the same destination. If a packet reaches the destination it is absorbed. The goal is to maximize the number of absorbed packets. Previous studies have shown that even on the line topology this problem is difficult to handle by online algorithms. A lower bound of Ω( √ n) on the competitiveness of the Greedy algorithm was presented by Aiello et al in [2]. All other known algorithms have a polynomial competitive ratio. In this paper we give the first O(log n) competitive deterministic algorithm for the information gathering problem in lines, rings and trees. We also consider multi-destination routing where the destination of a packet may be any node. For lines and rings we show an O(log 2 n) competitive randomized algorithms. Both for information gathering and for the multi-destination routing our results improve exponentially the previous results.

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“…In particular competitive analysis in which one has to deal with dropped packets becomes a common approach ( [2,17]). …”

Section: Introductionmentioning

confidence: 99%

Packet Routing and Information Gathering in Lines, Rings and Trees

Azar

Zachut

2005

Algorithms – ESA 2005

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“…In this model, α(≥ 1) is the ratio between the largest and the smallest values of packets. Azar et al [5] gave a lower bound of 1.366 − Θ(1/m) for a deterministic algorithm for any B. Azar et al [6] gave a 3-competitive deterministic algorithm for the preemptive case. Itoh et al [9] showed no non-preemptive algorithm can be better than 1 + 1/(α ln(α/(α − 1)))-competitive.…”

Section: Related Resultsmentioning

confidence: 99%

A Tight Upper Bound on Online Buffer Management for Multi-Queue Switches with Bicodal Buffers

Kobayashi

Miyazaki

Okabe

2008

IEICE Transactions on Information and Systems

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SUMMARYThe online buffer management problem formulates the problem of queuing policies of network switches supporting QoS (Quality of Service) guarantee. In this paper, we consider one of the most standard models, called multi-queue switches model. In this model, Albers et al. gave a lower bound e e−1 , and Azar et al. gave an upper bound e e−1 on the competitive ratio when m, the number of input ports, is large. They are tight, but there still remains a gap for small m. In this paper, we consider the case where m = 2, namely, a switch is equipped with two ports, which is called a bicordal buffer model. We propose an online algorithm called Segmental Greedy Algorithm (S G) and show that its competitive ratio is at most

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“…Thus, applying the result of Kesselman et al [12], they derived a 4-competitive algorithm for the general preemptive model, and by applying the result of Andelman et al [4], they derived a (2e ln α )-competitive algorithm for the general non-preemptive model. Recently, a 3-competitive algorithm was given for the preemptive case in [6].…”

Section: Side Resultsmentioning

confidence: 99%

Maximizing throughput in multi-queue switches

Azar

Litichevskey

2006

Algorithmica

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We study a basic problem in Multi-Queue switches. A switch connects m input ports to a single output port. Each input port is equipped with an incoming FIFO queue with bounded capacity B. A switch serves its input queues by transmitting packets arriving at these queues, one packet per time unit. Since the arrival rate can be higher than the transmission rate and each queue has limited capacity, packet loss may occur as a result of insufficient queue space. The goal is to maximize the number of transmitted packets. This general scenario models most current networks (e.g., IP networks) which only support a "best effort" service in which all packet streams are treated equally. A 2-competitive algorithm for this problem was designed in [5] for arbitrary B. Recently, a 17 9 ≈ 1.89-competitive algorithm was presented for B > 1 in [3]. Our main result in this paper shows that for B which is not too small our algorithm can do better than 1.89, and approach a competitive ratio of e e−1 ≈ 1.58.

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The zero-one principle for switching networks

Cited by 51 publications

References 28 publications

Packet Routing and Information Gathering in Lines, Rings and Trees

Packet Routing and Information Gathering in Lines, Rings and Trees

A Tight Upper Bound on Online Buffer Management for Multi-Queue Switches with Bicodal Buffers

Maximizing throughput in multi-queue switches

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