Approximation algorithms for the design of SDH/SONET networks

Brauner, Nadia; Crama, Yves; Finke, Gerd; Lemaire, Pierre; Wynants, Christelle

doi:10.1051/ro:2004003

Cited by 12 publications

(33 citation statements)

References 13 publications

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“…A graph partitioning formulation has been used to develop approximation algorithms [2,6] for this problem. In this formulation, a simple undirected graph G(V , E), called the traffic graph, is constructed to represent the set R of unitary duplex traffic demands, where the node set V (G) denotes the set of network nodes in the UPSR.…”

Section: Introductionmentioning

confidence: 99%

“…For a traffic graph G, their algorithm uses at most (1 + wavelengths, which is twice the minimum. Brauner et al [2] also proposed an approximation algorithm for the k-edge-partitioning problem. Their algorithm grooms traffic demands into the minimum number…”

Section: Introductionmentioning

confidence: 99%

“…One key observation is that given a fixed number of edges of G, a subgraph induced by the edges is more likely to contain fewer nodes if there are fewer connected components in the subgraph. This is the basic idea behind the algorithms in [2,6]. The algorithm in [6] guarantees that each subgraph is connected, while every subgraph might contain only k/2 edges in the worst case.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm in [6] guarantees that each subgraph is connected, while every subgraph might contain only k/2 edges in the worst case. The algorithm in [2] does not guarantee that each subgraph is connected; instead it guarantees that the total number of connected components over all subgraphs is bounded above and each subgraph contains exactly k edges.…”

Section: Introductionmentioning

confidence: 99%

“…Both algorithms utilize an idea similar to the algorithm in [2], and they guarantee that the total number of connected components over all subgraphs is bounded above. Our algorithms use at most (1+…”

Section: Introductionmentioning

confidence: 99%

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Minimizing SONET Add‐Drop Multiplexers in optical UPSR networks using the minimum number of wavelengths

Wang

2009

Networks

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In SONET/WDM optical networks, a high-speed wavelength channel is usually shared by multiplexed low-rate network traffic demands. The multiplexing is known as traffic grooming and carried out by SONET Add-Drop Multiplexers (SADM). The maximum number of low-rate traffic demands that can be multiplexed into one wavelength is called the grooming factor. Because SADMs are expensive network devices, a key optimization problem in optical network design is to groom a given set of low-rate traffic demands such that the number of required SADMs is minimized. This optimization problem is challenging and NP-hard even for Unidirectional Path-Switched Ring networks with unitary duplex traffic demands. In this article, we propose two linear-time approximation algorithms for this NP-hard problem based on a novel graph partitioning approach. Both algorithms achieve better worst case performance than the previous algorithms. We also show that the upper bounds obtained by our algorithms are very close to the lower bounds for some instances. In addition, both of our algorithms use the minimum number of wavelengths, which are precious resources as well in optical networks.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimizing SONET Add‐Drop Multiplexers in optical UPSR networks using the minimum number of wavelengths

Wang

2009

Networks

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Routing Algorithms on WDM Optical Networks

Nayak

2007

Handbook of Applied Algorithms

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The ring grooming problem

Chow

Lin²

2004

Networks

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The problem of minimizing the number of bidirectional SONET rings required to support a given traffic demand has been studied by several researchers. Here we study the related ring-grooming problem of minimizing the number of add/drop locations instead of the number of rings; in a number of situations this is a better approximation to the true equipment cost. Our main result is a new lower bound for the case of uniform traffic. This allows us to prove that a certain simple algorithm for uniform traffic is, in fact, a constant-factor approximation algorithm, and it also demonstrates that known lower bounds for the general problem-in particular, the linear programming relaxation-are not within a constant factor of the optimum. We also show that our results for uniform traffic extend readily to the more practically important case of quasi-uniform traffic. Finally, we show that if the number of nodes on the ring is fixed, then ring grooming is solvable in polynomial time; however, whether ring grooming is fixed-parameter tractable is still an open question.

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Approximation algorithms for the design of SDH/SONET networks

Cited by 12 publications

References 13 publications

Minimizing SONET Add‐Drop Multiplexers in optical UPSR networks using the minimum number of wavelengths

Minimizing SONET Add‐Drop Multiplexers in optical UPSR networks using the minimum number of wavelengths

Routing Algorithms on WDM Optical Networks

The ring grooming problem

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