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A review of routing and wavelength assignment approaches for wavelengthrouted optical WDM networks
 Optical Networks Magazine
, 2000
"... This study focuses on the routing and WavelengthAssignment (RWA) problem in wavelengthrouted optical WDM networks. Most of the attention is devoted to such networks operating under the wavelengthcontinuity constraint, in which lightpaths are set up for connection requests between node pairs, and ..."
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Cited by 235 (10 self)
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This study focuses on the routing and WavelengthAssignment (RWA) problem in wavelengthrouted optical WDM networks. Most of the attention is devoted to such networks operating under the wavelengthcontinuity constraint, in which lightpaths are set up for connection requests between node pairs, and a single lightpath must occupy the same wavelength on all of the links that it spans. In setting up a lightpath, a route must be selected and a wavelength must be assigned to the lightpath. If no wavelength is available for this lightpath on the selected route, then the connection request is blocked. We examine the RWA problem and review various routing approaches and wavelengthassignment approaches proposed in the literature. We also briefly consider the characteristics of wavelengthconverted networks (which do not have the wavelengthcontinuity constraint), and we examine the associated research problems and challenges. Finally, we propose a new wavelengthassignment scheme, called Distributed Relative Capacity Loss (DRCL), which works well in distributedcontrolled networks, and we demonstrate the performance of DRCL through simulation. 1
The Partition Coloring Problem and its Application to Wavelength Routing and Assignment
 In Proceedings of the First Workshop on Optical Networks
, 2000
"... We consider a new vertex coloring problem, that we call partitioncoloring, in which the vertex set of a graph G = (V; E) is partitioned into k disjoint sets V = V 1 [ \Delta \Delta \Delta [V k , and G is said to be partitioncolored if exactly one v in each V i is colored and every two adjacent col ..."
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Cited by 16 (0 self)
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We consider a new vertex coloring problem, that we call partitioncoloring, in which the vertex set of a graph G = (V; E) is partitioned into k disjoint sets V = V 1 [ \Delta \Delta \Delta [V k , and G is said to be partitioncolored if exactly one v in each V i is colored and every two adjacent colored vertices have different colors. Analogous to the standard vertex coloring problem, we wish to partitioncolor a given graph with as few colors as possible. The partitioncoloring problem is motivated by the wavelength routing and assignment problem in WDM (Wavelength Division Multiplexing) optical networks. In this paper, we show that this new coloring problem is as hard as standard vertex coloring and investigate heuristic algorithms. An application of these heuristics to the wavelength routing and assignment problem on optical networks is studied via simulation. Keywords: graph coloring, wavelength assignment, optical networks, routing. 1 Introduction We define and study a new grap...
A branchandcut algorithm for partition coloring
 In Proceedings of The International Network Optimization Conference
, 2007
"... Let G = (V,E,Q) be a undirected graph, where V is the set of vertices, E is the set of edges, and Q = {Q1,..., Qq} is a partition of V into q subsets. We refer to Q1,..., Qq as the components of the partition. The Partition Coloring Problem (PCP) consists of finding a subset V ′ of V with exactly on ..."
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Let G = (V,E,Q) be a undirected graph, where V is the set of vertices, E is the set of edges, and Q = {Q1,..., Qq} is a partition of V into q subsets. We refer to Q1,..., Qq as the components of the partition. The Partition Coloring Problem (PCP) consists of finding a subset V ′ of V with exactly one vertex from each component Q1,..., Qq and such that the chromatic number of the graph induced in G by V ′ is minimum. This problem is a generalization of the graph coloring problem. This work presents a branchandcut algorithm proposed for PCP. An integer programming formulation and valid inequalities are proposed. A tabu search heuristic is used for providing primal bounds. Computational experiments are reported for random graphs and for PCP instances originating from the problem of routing and wavelength assignment in alloptical WDM networks.
On Bounds for the Wavelength Assignment Problem on Optical Ring Networks.
 Journal of HighSpeed Networks
, 1999
"... : This research note presents two new bounds for the offline wavelength assignment problem in optical ring networks that use wavelength division multiplexing. In this context, we consider a wellknown bound [28, 35] that, to our knowledge, remains the only published bound for a ring topology and for ..."
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Cited by 4 (2 self)
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: This research note presents two new bounds for the offline wavelength assignment problem in optical ring networks that use wavelength division multiplexing. In this context, we consider a wellknown bound [28, 35] that, to our knowledge, remains the only published bound for a ring topology and for which examples exist that show tightness. In this note, we show the bound can be improved in two ways: (1) by considering an additional parameter (the number of network nodes), we provide a sharper bound than the existing bound, and (2) we extend a classic result in [35] that was proved for the special case of k = 3 (no k connections cover the ring) to the general case of arbitrary k. Keywords: optical networks, wavelength division multiplexing, wavelength assignment problems. 1 Introduction The wavelength assignment problem is usually framed as follows: given a set of connections, find the minimum number of wavelengths needed to transmit the connections simultaneously so that no two con...
On the Chromatic Number of Graphs
 Journal of Optimization Theory and Applications
, 2001
"... Computing the chromatic number of a graph is an NPhard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 01 integer programming formulation for the graph coloring problem is presented. The prop ..."
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Cited by 1 (1 self)
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Computing the chromatic number of a graph is an NPhard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 01 integer programming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates graphs of known chromatic number by using the KKT optimality conditions of a related continuous nonlinear program.
Algoritmo de Branch and Cut para el
"... A Isabel y Paula, mis directoras, no solamente por la guía indispensable que fueron para el desarrollo de este trabajo (con notable paciencia), sino por haberme enseñado todo lo que sé acerca de Métodos Numéricos e Investigación Operativa, y haberme transmitido su gran pasión por estas áreas. Su tra ..."
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A Isabel y Paula, mis directoras, no solamente por la guía indispensable que fueron para el desarrollo de este trabajo (con notable paciencia), sino por haberme enseñado todo lo que sé acerca de Métodos Numéricos e Investigación Operativa, y haberme transmitido su gran pasión por estas áreas. Su trabajo y dedicación como directoras es solamente comparable a su desempeño como las excelentes docentes que son. A Irene Loiseau y Esteban Feuerstein, por haber aceptado ser jurados de este trabajo, y por las correcciones que permitieron concluirlo como corresponde. A todo el Departamento de Computación de la Facultad de Ciencias Exactas y Naturales de la UBA, especialmente a sus docentes, por haberme brindado una educación excelente y gratuita; así como a los grupos de Algoritmos y Métodos Numéricos, por darme un espacio como ayudante en el cual devolver una pequeña parte de lo aprendido. A mis compañeros de la cursada, la gentedelafacu, junto a quienes recorrí la carrera y a quienes les debo las alegrías dentro de la facultad en estos
Section 8.1 Vertex Independence and Coverings
"... Next, we consider a problem that strikes close to home for us all, final exams. At the end of each term, students are required to take final exams in each of their classes. Each exam is to be given once during some specified period, and the time allowed for each exam (no matter what the class) is th ..."
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Next, we consider a problem that strikes close to home for us all, final exams. At the end of each term, students are required to take final exams in each of their classes. Each exam is to be given once during some specified period, and the time allowed for each exam (no matter what the class) is the same. The question of interest is: What is the minimum number of examination periods needed to ensure there are no conflicts, that is, that no student has two exams during the same period. Of course, as you well know, this is a completely fictional problem since no school has ever tried to determine this number. As usual, we desire a graph model for this problem. Thus, we seek a graph G = (V, E) where each vertex of V represents an examination and xy ∈ E if, and only if, there is some student that must take both examination x and examination y. Two examinations can be scheduled in the same period only if there is no edge between the corresponding vertices in our model. Thus, we seek sets of mutually nonadjacent vertices in G; that is, we seek independent sets of vertices. A solution to our problem is a partitioning of V into sets of mutually independent vertices where the number of such sets is a minimum. Vertices in the same set of this partition represent exams that can be