Efficient routing in optical networks

Aggarwal, Alok; Bar-Noy, Amotz; Coppersmith, Don; Ramaswami, Rajiv; Schieber, Baruch; Sudan, Madhu

doi:10.1145/235809.235812

Cited by 93 publications

(93 citation statements)

References 10 publications

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“…If not, the flow routing problems in different time slots become dependent, yielding to a more complex problem. Some suitable heuristics have been proposed in the literature which could be then used in this Step [13], [14].…”

Section: Step 3 Variable Flow Routing Calculationmentioning

confidence: 99%

Virtual topology design and flow routing in optical networks under multihour traffic demand

et al. 2009

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This paper addresses the problem of finding a static virtual topology design and flow routing in transparent optical WDM networks under a time-varying (multi-hour) traffic demand. Four variants of the problem are considered, using fixed or dynamically adaptable (i.e., variable) flow routing, which can be splittable or unsplittable. Our main objective is to minimize the number of transceivers needed which make up for the main network cost. We formulate the problem variants as exact ILPs (Integer Linear Programs) and MILPs (Mixed ILPs). For larger problem instances, we also propose a family of heuristics based on the concept of domination between traffic matrices. This concept provides the theoretical foundations for a set of techniques proposed to reduce the problem complexity. We present a lower bound to the network cost for the case in which the virtual topology could be dynamically reconfigured along time. This allows us to assess the limit on the maximum possible benefit that could be achieved by using optical reconfigurable equipment. Extensive tests have been conducted, using both synthetically generated and real-traced traffic demands. In the cases studied, results show that combining variable routing with splittable flows obtains a significant, although moderate, cost reduction. The maximum cost reduction achievable with reconfigurable virtual topologies was shown to be negligible compared to the static case in medium and high loads.

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Section: Step 3 Variable Flow Routing Calculationmentioning

confidence: 99%

Virtual topology design and flow routing in optical networks under multihour traffic demand

et al. 2009

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“…Aggarwal et al [2] provided a polynomial time algorithm that can find a matching of size n against any adversary provided that the graph H is such that, for every X ⊆ U with |X| ≤ n, even after at most half the edges incident to every vertex of X are removed, there remains at least 2|X| neighbors of X. This result is given by the theorem below.…”

Section: Online Games and Tree Embeddingsmentioning

confidence: 99%

“…Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem.We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters.Our algorithmic approach is based on a reduction of the tree embedding problem to a certain online matching problem for bipartite graphs, solved by Aggarwal et al (1996). …”

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confidence: 99%

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An algorithmic Friedman--Pippenger theorem on tree embeddings and applications to routing

Dellamonica

Kohayakawa

2006

Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm - SODA '06

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Abstract. An (n, d)-expander is a graph G = (V, E) such that for every X ⊆ V with |X| ≤ 2n − 2 we have |Γ G (X)| ≥ (d + 1)|X|. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any (n, d)-expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, λ)-graphs Λ, as long as G contains a positive fraction of the edges of Λ and λ/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, λ)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem.We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters.Our algorithmic approach is based on a reduction of the tree embedding problem to a certain online matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

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“…As there is no fixed infrastructure between wireless sensor networks for communication, routing becomes an issue in large number of sensor nodes deployed along with other challenges of manufacturing, design and reliability of these networks [5][6][7][8]. The main issue of concern in this paper is Reliability.…”

Section: Introductionmentioning

confidence: 99%