The ring grooming problem

Chow, Timothy Y.; Lin, Pao Tai

doi:10.1002/net.20029

Cited by 30 publications

(19 citation statements)

References 21 publications

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“…Notice that by construction each node in the ring must have at least one transceiver; if there are exactly transceivers then this bound is meet with equality. With , from (8), it follows that the corresponding edge coloring of satisfies for all and , i.e., this must be a proper edge coloring of with colors. And so, from Vizing's theorem, the chromatic index must be .…”

Section: Complexity Resultsmentioning

confidence: 99%

“…This is because in the MTPS problem both circuits in a duplex connection are always assigned to the same wavelength/time-slot. In this case (8) Note that a feasible solution to the MTP problem cannot be identified with an edge coloring of , unless it is also a feasible solution to the MTPS problem. 7 This edge coloring representation of a solution to the MTP or MTPS problem indicates the time-slot for each circuit but does not indicate the wavelength that the circuit is assigned to.…”

Section: Graph Theoretic Formulationsmentioning

confidence: 99%

“…This will require wavelengths. It follows that any edge coloring of with colors gives a feasible solution to the MTP and MTPS problems with available wavelengths if and only if (9) Therefore, the MTPS problem can be viewed completely in terms of finding an edge coloring of that satisfies (9) and minimizes (8). On the other hand, for the MTP problem we must, in general, consider edge colorings of .…”

Section: Graph Theoretic Formulationsmentioning

confidence: 99%

“…In [22], the following relationship between equitable and equalized edge coloring is given. 8 Theorem 1: If a multigraph has an equitable edge coloring with colors, then there exists an edge coloring with colors that is both equalized and equitable.…”

Section: Graph Theoretic Formulationsmentioning

confidence: 99%

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Satellite Data Networks

Modiano

2004

Journal of Aerospace Computing, Information, and Communication

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Abstract-In this paper, we study the benefits of using tunable transceivers for reducing the required number of electronic ports in wavelength-division-multiplexing/time-division multiplexing optical networks. We show that such transceivers can be used to efficiently "groom" subwavelength traffic in the optical domain and so can significantly reduce the amount of terminal equipment needed compared with the fixed-tuned case. Formulations for this "tunable grooming" problem are provided, where the objective is to schedule transceivers so as to minimize the required number of ports needed for a given traffic demand. We establish a relationship between this problem and edge colorings of graphs which are determined by the offered traffic. Using this relationship, we show that, in general, this problem is NP-complete, but we are able to efficiently solve it for many cases of interest. When the number of wavelengths in the network is not limited, each node is shown to only require the minimum number of transceivers (i.e., no more transceivers than the amount of traffic that it generates). This holds regardless of the network topology or traffic pattern. When the number of wavelengths is limited, an analogous result is shown for both uniform and hub traffic in a ring. We then develop a heuristic algorithm for general traffic that uses nearly the minimum number of transceivers. In most cases, tunable transceivers are shown to reduce the number of ports per node by as much as 60%. We also consider the case where traffic can dynamically change among an allowable set of traffic demands. Tunability is again shown to significantly reduce the port requirement for a nonblocking ring, both with and without rearrangements.Index Terms-Graph coloring, integer linear programming (ILP), optical networks, traffic grooming, wavelength-division multiplexing (WDM).

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Section: Complexity Resultsmentioning

confidence: 99%

Section: Graph Theoretic Formulationsmentioning

confidence: 99%

Section: Graph Theoretic Formulationsmentioning

confidence: 99%

Section: Graph Theoretic Formulationsmentioning

confidence: 99%

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Satellite Data Networks

Modiano

2004

Journal of Aerospace Computing, Information, and Communication

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“…a SONET ADM). The basic traffic grooming problem as studied in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] is to assign a given traffic requirement to wavelengths so that the total number of needed ports are minimized. The general traffic grooming problem has been shown to be NP-complete [1], even in the special case where all traffic is sent to a single egress node.…”

Section: Introductionmentioning

confidence: 99%

On the benefit of tunability in reducing electronic port counts in WDM/TDM networks

Berry

Modiano

Ieee Infocom 2004

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Abstract-In this paper, we study the benefits of using tunable transceivers for reducing the required number of electronic ports in WDM/TDM networks. We show that such transceivers can be used to efficiently "groom" sub-wavelength traffic in the optical domain and so can significantly reduce the number of electronic ports compared to the fixed tuned case. We provide a new formulation for this "tunable grooming" problem. We show that in general this problem is NP-complete, but we are able to efficiently solve it for many cases of interest. When the number of wavelengths in the network is not limited, we show that each node only needs the minimum number of transceivers (i.e., no more transceivers than the amount of traffic that it generates). This holds regardless of the network topology or traffic pattern. When the number of wavelengths is limited, we show an analogous result for both uniform and hub traffic in a ring. We also develop a heuristic algorithm for general traffic that uses nearly the minimum number of transceivers. In most cases, tunable transceivers are shown to reduce the number of ports per node by as much as 60%.

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Traffic grooming in bidirectional WDM ring networks

Bermond

Muñoz

2010

Networks

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International audienceWe study the minimization of ADMs (Add-Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all-to-all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor C and N, the size of the ring. We first study exhaustively the cases C = 1, C = 2, and C = 3, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case C > 3, focusing specifically on the case C = k(k + 1)/2 for some k ≥ 1. We give optimal decompositions for several congruence classes of N using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings

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The ring grooming problem

Cited by 30 publications

References 21 publications

Satellite Data Networks

Satellite Data Networks

On the benefit of tunability in reducing electronic port counts in WDM/TDM networks

Traffic grooming in bidirectional WDM ring networks

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