Topological properties for a wide area network planning and a dynamic programming approach for designing the access network

A wide area network (WAN) can be considered as a set of sites and a set of communication lines that interconect the sites. Topologically a WAN is organized in two levels: the Backbone Network and the Access Network composed of a certain number of Local Access Network. Each local access network usually has a tree-like structure, rooted at a single site of the backbone, and connected users (terminal sites) either directly to this backbone site or to a hierarchy of intermediate concentrator sites which are connected to the backbone site. The backbone network has usually a meshed topology, and this purpose is to allow efficient and reliable communication between the switch sites that act as connection points for the local access networks. In this thesis we tackled the problem of designing a WAN by breaking it down into two inter-related sub-problems: the Access Network Design Problem (ANDP) and the Backbone Network Design Problem (BNDP). In both models we considered only the construction costs, e.g. the costs of digging trenches and placing a fiber cable into service. Our aim in this thesis is the study of the ANDP and the BNDP problems. We concentrate on the ANDP with the objective of to propose a new approach for solving this problem. We study differents results related to the topological structure of the ANDP solutions. We present the clustering approach as one of the strategies more frequently used by the commercial tools of the design. We also formulate the ANDP as a Steiner Problem in Graphs (SPG). Given the complexity of the ANDP (the problem belongs to the NP-Hard class); it is very useful to provide techniques capable of reducing the dimension of the original problem to an equivalent smaller problem. After we concentrate on some structural property about the BNDP. Finally we propose recurrences to solve the ANDP and BNDP which are based on Dynamic Programming and Dynamic Programming with Static-Space Relaxation methodology.Una red de área extendida (Wide Area Network - WAN) puede ser considerada como un conjunto de sitios interconectados por líneas de comunicación. Topológicamente una red WAN esta organizada en dos niveles: la Red Dorsal (Backbone) y la Red de Acceso (Access Network) compuesta por un cierto número de Redes de Acceso Locales. Cada red de acceso local usualmente tiene topología de árbol, teniendo como raíz un nodo de la Red Dorsal (sitio dorsal). Los sitios terminales (o clientes) se conectan directamente al sitio dorsal correspondiente a una red de acceso o bien a un sitio concentrador de la misma. La Red Dorsal tiene usualmente topología de malla y su propósito es permitir comunicación eficiente y confiable entre nodos de la Red Dorsal que actúan como puntos de entrada para las Redes de Acceso Locales. En esta tesis atacamos el problema del diseño de una red WAN descomponiéndola en dos sub-problemas interrelacionados: el diseño de la Red de Acceso (the Access Network Design Problem - ANDP) y el diseño de la Red Dorsal (the Backbone Network Design Problem - BNDP). En ambos modelos consideramos solamente los costos de construcción, por ejemplo, los costos de dragados para el tendido de líneas y la puesta en servicio del cableado de la red. Nuestro objetivo es estudiar los problemas ANDP y BNDP. Nos concentramos en ANDP con el objetivo de proponer un nuevo enfoque para resolverlo. Introducimos diferentes resultados en lo que concierne a las propiedades estructurales de las soluciones del ANDP. Presentamos el enfoque de clúster como una de las estrategias más usadas por las herramientas comerciales de diseño. Modelamos el ANDP como una variante del Problema de Steiner en Gráfos (the Steiner Problem in Graphs - SPG). Dada la complejidad del problema (es NPHard); es útil proveer técnicas para reducir la dimensión del problema original en uno equivalente de menor tamaño.Luego nos concentramos en algunas propiedades estructurales de las soluciones óptimas del BNDP. Finalmente proponemos recurrencias para resolver los problemas ANDP y BNDP basadas en las metodologías de Programación Dinámica y Programación Dinámica con Relajación del Espacio de Estados

An efficient algorithm for nucleolus and prekernel computation in some classes of TU-games

We consider classes of TU-games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel. \u