The Network as a Storage Device: Dynamic Routing with Bounded Buffers

Angelov, Stanislav; Khanna, Sanjeev; Kunal, Keshav

doi:10.1007/11538462_1

Cited by 8 publications

(14 citation statements)

References 15 publications

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“…In the case that deadlines need to be met the approximation ratio is, roughly, O(log * n) [RR11]. As a final example, one can obtain from [AKK09] various online distributed algorithms with sublinear competitive ratios w.r.t. throughput maximization.…”

Section: High-level Overviewmentioning

confidence: 99%

Robust Routing Made Easy

Lenzen

Medina

2017

Lecture Notes in Computer Science

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Designing routing schemes is a multidimensional and complex task that depends on the objective function, the computational model (centralized vs. distributed), and the amount of uncertainty (online vs. offline). Nevertheless, there are quite a few well-studied general techniques, for a large variety of network problems. In contrast, in our view, practical techniques for designing robust routing schemes are scarce; while fault-tolerance has been studied from a number of angles, existing approaches are concerned with dealing with faults after the fact by rerouting, selfhealing, or similar techniques. We argue that this comes at a high burden for the designer, as in such a system any algorithm must account for the effects of faults on communication.With the goal of initiating efforts towards addressing this issue, we showcase simple and generic transformations that can be used as a blackbox to increase resilience against (independently distributed) faults. Given a network and a routing scheme, we determine a reinforced network and corresponding routing scheme that faithfully preserves the specification and behavior of the original scheme. We show that reasonably small constant overheads in terms of size of the new network compared to the old are sufficient for substantially relaxing the reliability requirements on individual components. The main message in this paper is that the task of designing a robust routing scheme can be decoupled into (i) designing a routing scheme that meets the specification in a fault-free environment, (ii) ensuring that nodes correspond to fault-containment regions, i.e., fail (approximately) independently, and (iii) applying our transformation to obtain a reinforced network and a robust routing scheme that is fault-tolerant.likely that none of them fail. Existing designs and algorithms (that are considered practical) do account for lost messages and, in some cases, permanently crash-failing nodes or edges [CLM12, KKD10, PNK + 06].It is our understanding that handling stronger fault types is considered practically infeasible, be it in terms of complexity of implementations or the involved overheads. However, pretending that crash failures are the worst that can happen means that the entire system possibly fails whenever, e.g., we face a "babbling idiot" (i.e., a node erroneously generating many messages and congesting the network), excessive link delays (violating specification), or misrouting, corruption, or loss of messages. The current approach is to (i) use techniques like error correction, acknowledging reception, etc. to mask the effects of such faults, (ii) hope to detect and deactivate faulty components quickly (logically mapping faults to crashes), and (iii) repair or replace the faulty components after they have been taken offline. This strategy may result in significant disruption of applications; possible consequences include:(I) Severe delays in execution, as successful message delivery necessitates to detect and deactivate faulty components first. (II) Failure to deliver cor...

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Section: High-level Overviewmentioning

confidence: 99%

Robust Routing Made Easy

Lenzen

Medina

2017

Lecture Notes in Computer Science

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“…In [3], a lower bound of Ω( √ n) was proved for the greedy algorithm on unidirectional lines if the buffer size B ≥ 2. For the case B = 1 (in a slightly different model), an Ω(n) lower bound for any deterministic algorithm was proved by [7,4]. Both [7] and [4] developed, among other things, online randomized centralized algorithms for uni-directional lines with B ≥ 2.…”

Section: Previous Workmentioning

confidence: 99%

“…For the case B = 1 (in a slightly different model), an Ω(n) lower bound for any deterministic algorithm was proved by [7,4]. Both [7] and [4] developed, among other things, online randomized centralized algorithms for uni-directional lines with B ≥ 2. In [4] an O(log 3 n)-competitive randomized centralized algorithm was presented for B ≥ 2.…”

Section: Previous Workmentioning

confidence: 99%

“…Both [7] and [4] developed, among other things, online randomized centralized algorithms for uni-directional lines with B ≥ 2. In [4] an O(log 3 n)-competitive randomized centralized algorithm was presented for B ≥ 2. In addition, it is proved in [4] that nearest-to-go isÕ( √ n)-competitive for B ≥ 2.…”

Section: Previous Workmentioning

confidence: 99%

“…In [4] an O(log 3 n)-competitive randomized centralized algorithm was presented for B ≥ 2. In addition, it is proved in [4] that nearest-to-go isÕ( √ n)-competitive for B ≥ 2. For the case B = 1, [4] presented a randomizedÕ( √ n)-competitive distributed algorithm.…”

Section: Previous Workmentioning

confidence: 99%

See 2 more Smart Citations

Better Deterministic Online Packet Routing on Grids

Even

Medina

Patt-Shamir

2015

Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures

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We consider the following fundamental routing problem. An adversary inputs packets arbitrarily at sources, each packet with an arbitrary destination. Traffic is constrained by link capacities and buffer sizes, and packets may be dropped at any time. The goal of the routing algorithm is to maximize throughput, i.e., route as many packets as possible to their destination. Our main result is an O (log n)-competitive deterministic algorithm for an n-node uni-directional line network (i.e., 1-dimensional grid), requiring only that buffers can store at least 5 packets, and that links can deliver at least 5 packets per step. We note that O(log n) is the best ratio known, even for randomized algorithms, even when allowed large buffers and wide links. The best previous deterministic algorithm for this problem with constant-size buffers and constant-capacity links was O(log 5 n)-competitive. Our algorithm works like admission-control algorithms in the sense that if a packet is not dropped immediately upon arrival, then it is "accepted" and guaranteed to be delivered. We also show how to extend our algorithm to a polylog-competitive algorithm for any constant-dimension uni-directional grid.

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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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The Network as a Storage Device: Dynamic Routing with Bounded Buffers

Cited by 8 publications

References 15 publications

Robust Routing Made Easy

Robust Routing Made Easy

Better Deterministic Online Packet Routing on Grids

Packet Routing and Information Gathering in Lines, Rings and Trees

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