Maximizing Throughput in Multi-queue Switches

Azar, Yossi; Litichevskey, Arik

doi:10.1007/978-3-540-30140-0_7

Cited by 35 publications

(46 citation statements)

References 12 publications

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“…3 and 4) is a construction that shows that no fractional algorithm may achieve a competitive ratio lower than e/(e − 1) ≈ 1.582 for any value of B and for large m. This result has a few implications (see also Table 1): -The result is up to lower-order terms optimal; it matches the performance of the fractional algorithm FRAC-WATERLEVEL of [7]. It also gives evidence that the reduction of Azar and Litichevskey from the online fractional bipartite matching to the fractional packet buffering was essentially tight.…”

Section: Our Contributionmentioning

confidence: 66%

“…Our construction yields the same ratio, but requires only that m is large; B may be arbitrary, e.g., even much larger than m. Thus, in contrast to their construction, ours shows that the deterministic algorithm DET-WATERLEVEL [7] achieves the asymptotically optimal competitive ratio when both m is large and B log m.…”

Section: Our Contributionmentioning

confidence: 70%

“…5) that any randomized algorithm can be simulated by a fractional one without increasing its competitive ratio, i.e., the fractional model is "easier" for algorithms and "harder" for the adversary. A relaxed relation in the opposite direction also exists: Azar and Litichevskey showed how to transform a c-competitive fractional solution into a deterministic c · (1 + H m + 1 /B)-competitive one [7].…”

Section: Previous Workmentioning

confidence: 99%

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An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

Bieńkowski

2012

Algorithmica

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In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets from input ports to the output port. Buffers attached to input ports may accumulate incoming packets for later transmission; if they cannot accommodate all incoming packets, their excess is lost. A packet buffering algorithm has to choose from which buffers to transmit packets in order to minimize the number of lost packets and thus maximize the throughput.We present a tight lower bound of e/(e − 1) ≈ 1.582 on the competitive ratio of the throughput maximization, which holds even for fractional or randomized algorithms. This improves the previously best known lower bound of 1.4659 and matches the performance of the algorithm RANDOM SCHEDULE. Our result contradicts the claimed performance of the algorithm RANDOM PERMUTATION; we point out a flaw in its original analysis.

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Section: Our Contributionmentioning

confidence: 66%

Section: Our Contributionmentioning

confidence: 70%

Section: Previous Workmentioning

confidence: 99%

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An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

Bieńkowski

2012

Algorithmica

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“…The first usage is: given an algorithm for problem A we can obtain an algorithm for problem B by combining an appropriate reduction function which maps instances of B to instances of A, then use a good algorithm for A. On the other hand, if we have a lower bound for problem B, we inherit the same lower bound for problem A from a reduction from B to A. Online reductions have been used to design algorithms in, for example, [AL04], which solves a fractional version of a Maximizing Switch Throughput problem and then reduces the more interesting discrete version to the fractional version. Unlike in complexity, online reductions have rarely been used to compare the likely hardness of online algorithms, probably because researchers have been successful at proving lower bounds directly.…”

Section: Reductions Between Online Problemsmentioning

confidence: 99%

“…Although online reductions were used before our work (See [AL04]) as a general technique for obtaining new online algorithms from algorithms for other problems and we used it in similar fashion in Sect. 3, to our knowledge our work is the first that uses the notion of reduction between online algorithms to prove lower bounds on competitive ratio and relate hardness of one problem to that of another (Sect.…”

Section: Future Workmentioning

confidence: 99%

Online Algorithms to Minimize Resource Reallocations and Network Communication

Davis

Edmonds

Impagliazzo

2006

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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Abstract. In this paper, we consider two new online optimization problems (each with several variants), present similar online algorithms for both, and show that one reduces to the other. Both problems involve a control trying to minimize the number of changes that need to be made in maintaining a state that satisfies each of many users' requirements. Our algorithms have the property that the control only needs to be informed of a change in users needs when the current state no longer satisfies the user. This is particularly important when the application is one of trying to minimize communication between the users and the control. The Resource Allocation Problem (RAP) is an abstraction of scheduling malleable and evolving jobs on multiprocessor machines. A scheduler has a fixed pool of resources of total size T . There are n users, and each user j has a resource requirement for rj,t resources. The scheduler must allocate resources j,t to user j at time t such that each allocation satisfies the requirement (rj,t ≤ j,t) and the combined allocations do not exceed T ( P j j,t ≤ T ). The objective is to minimize the total number of changes to allocated resources (the number of pairs j, t where j,t = j,t+1). We consider online algorithms for RAP whose resource pool is increased to sT and obtain an online algorithm which is O(log s n) competitive. Further we show that the increased resource pool is crucial to the performance of the algorithm by proving that there is no online algorithm using T resources which is f (n)-competitive for any f (n). Note that our upper bounds all have the property that the algorithms only know the list of users whose requirements are currently unsatisfied and never learn the precise requirements of users. We feel this is important for many applications, since users rarely report underutilized resources as readily as they do unmet requirements. On the other hand, our lower bounds apply to online algorithms that have complete knowledge about past requirements. The Transmission-Minimizing Approximate Value problem is a generalization of one defined in [OLW01], in which low-power sensors monitor real-time events in a distributed wireless network and report their results to a centralized cache. In order to minimize network traffic, the cache is allowed to maintain approximations to the values at the sensors, inResearch partially supported by NSF Award CCR-0515332, but views expressed are not endorsed by the NSF. Research partially supported by NSF Award CCR-0515332, but views expressed are not endorsed by the NSF. the form of intervals containing the values, and to vary the lengths of intervals for the different sensors so that sensors with fluctuating values are measured less precisely than more stable ones. A constraint for the cache is that the sum of the lengths of the intervals must be within some precision parameter T . Similar models are described in [CYV04,cKA02]. We adapt the online randomized algorithm for the RAP problem to solve TMAV problem with similar competitive ratio: an algori...

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Packet Routing and Information Gathering in Lines, Rings and Trees

Azar

Zachut

2005

Algorithms – ESA 2005

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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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Maximizing Throughput in Multi-queue Switches

Cited by 35 publications

References 12 publications

An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

Online Algorithms to Minimize Resource Reallocations and Network Communication

Packet Routing and Information Gathering in Lines, Rings and Trees

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