Improving spanning trees by upgrading nodes

We study budget constrained optimal network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. A general problem in this setting is the following. We are given an edge weighted graph G = (V, E) where nodes represent processors and edges represent bidirectional communication links. The processor at a node v {element_of} V can be upgraded at a cost of c(v). Such an upgrade reduces the delay of each link emanating from v. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has the best performance with respect to some measure. We consider the problem under two measures, namely, the weight of a minimum spanning tree and the bottleneck weight of a minimum bottleneck spanning tree. We present approximation and hardness results for the problem. Our results are tight to within constant factors. We also show that these approximation algorithms can be used to construct good approximation algorithms for the dual versions of the problems where there is a budget constraint on the upgrading cost and the objectives are minimum weight spanning tree and minimum bottleneck weight spanning tree respectively

Problema geométrico conexo de localização de instalações

Orientadores: Flávio Keidi Miyazawa, Rafael Crivellari Saliba SchoueryDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Esse trabalho visa estudar problemas da família Localização de Instalações. Nesses problemas, recebemos de entrada um conjunto de clientes e um conjunto de instalações. Queremos encontrar e abrir um subconjunto de instalações, normalmente, pagando um preço por cada instalação aberta. Nosso objetivo é conectar clientes a instalações abertas, pagando o menor custo possível. Esse problema tem grandes aplicações na área de Pesquisa Operacional e Telecomunicações. Estamos especialmente interessados no problema de Localização de Instalações Geométrico e Conexo. Nessa versão do problema, as instalações podem ser abertas em qualquer lugar de um plano de dimensão d, e pagamos um preço fixo f por cada instalação aberta. Também devemos conectar as instalações entre si formando uma árvore. Essa árvore normalmente recebe uma ponderação maior, uma vez que suas conexões agregam atendimento para quantidade maior de recursos. Para representar tal ponderação seus custos são multiplicados por um parametro M > 0 dado como parte da entrada. Apresentamos um Esquema de Aproximação Polinomial para a versão euclidiana do problemaAbstract: In this work we study problems from the facility location family. In this set of problems, we want to find and open a subset of given facilities. Usually, a price is paid for each opened facility. Our goal is to connect given clients to the closest opened facilities incurring in the smallest cost possible. This problem has several practical applications in Operations Research and Telecommunication. We are specially interested in the Geometric Connected Facility Location problem. In this version, facilities can be anywhere in the d-dimensional plane, and we have to pay a fixed price f to open each facility. We also have the requirement of connecting facilities among themselves forming a tree. This tree is usually weighted by a given parameter M > 0. We present a Polynomial-Time Approximation Scheme for the two-dimensional version of this problemMestradoCiência da ComputaçãoMestra em Ciência da Computação1406904, 1364124CAPE

Issues in a very large scale distributed virtual environment.

So, King-yan Oldfield.Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.Includes bibliographical references (leaves 68-70).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Evolution of Communication Technologies --- p.1Chapter 1.2 --- The Internet --- p.2Chapter 1.3 --- The Distributed Virtual Environments --- p.2Chapter 1.3.1 --- Features of DVE --- p.3Chapter 1.3.2 --- Current and Potential Applications --- p.4Chapter 1.3.3 --- The Challenges --- p.5Chapter 1.4 --- Our Contributions --- p.6Chapter 2 --- System Architecture --- p.7Chapter 2.1 --- The SSDVE and MSDVE Architectures --- p.7Chapter 2.2 --- Issues in the MSDVE Architecture --- p.8Chapter 2.2.1 --- On the Server Side --- p.8Chapter 2.2.2 --- On the Client Side --- p.8Chapter 3 --- Balancing Work Load and Reducing Inter-server Communication --- p.10Chapter 3.1 --- Problem Formulation --- p.10Chapter 3.1.1 --- The Area of Interest --- p.11Chapter 3.1.2 --- The DVE Cells --- p.11Chapter 3.1.3 --- Expected Number of Avatars --- p.12Chapter 3.1.4 --- Cost Metrics in Different Types of Network --- p.13Chapter 3.1.5 --- Problem Definition --- p.14Chapter 3.1.6 --- Complexity --- p.18Chapter 3.2 --- Partitioning Algorithms --- p.19Chapter 3.2.1 --- A Simplified Case --- p.19Chapter 3.2.2 --- The General Case --- p.19Chapter 3.3 --- Experiments --- p.22Chapter 4 --- Communication Sub-graph --- p.31Chapter 4.1 --- Problem Formulation --- p.31Chapter 4.1.1 --- Optimization Metrics --- p.32Chapter 4.1.2 --- Design Considerations --- p.32Chapter 4.2 --- Communication Sub-graph Construction Algorithms --- p.34Chapter 4.2.1 --- The Minimum Diameter Sub-graph (MDS) --- p.34Chapter 4.2.2 --- The Core-based Tree (CBT) --- p.37Chapter 4.2.3 --- The Minimum Spanning Tree (MST) --- p.40Chapter 5 --- Synchronization --- p.42Chapter 5.1 --- Synchronization in a DVE System --- p.43Chapter 5.2 --- System Model --- p.46Chapter 5.2.1 --- Problem Definition --- p.47Chapter 5.2.2 --- The Markov Chain Model --- p.47Chapter 5.2.3 --- Deciding the Threshold Φ --- p.49Chapter 5.3 --- Optimal Synchronizing Interval --- p.50Chapter 5.3.1 --- "An ""on-average"" Guarantee" --- p.50Chapter 5.3.2 --- A Stochastic Guarantee --- p.52Chapter 5.3.3 --- Finding p with T and Φ --- p.52Chapter 5.3.4 --- Searching for r*p --- p.54Chapter 5.4 --- Experiments --- p.55Chapter 5.4.1 --- Simulation Results --- p.55Chapter 5.4.2 --- Theoretical Results --- p.58Chapter 6 --- Related Work --- p.63Chapter 6.1 --- Load Balancing on DVE --- p.63Chapter 6.2 --- Object State Synchronization Techniques --- p.63Chapter 6.3 --- Group Communication and Multicasting --- p.64Chapter 6.4 --- DVE System Development Toolkits --- p.64Chapter 6.5 --- Example DVE Systems --- p.65Chapter 7 --- Conclusion --- p.66Chapter 7.1 --- A Vision to the Future --- p.66Chapter 7.2 --- Conclusion --- p.66Bibliography --- p.6

Robust optimization, game theory, and variational inequalities

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 193-109).We propose a robust optimization approach to analyzing three distinct classes of problems related to the notion of equilibrium: the nominal variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand uncertainty. In the first part of the thesis, we demonstrate that the nominal VI problem is in fact a special instance of a robust constraint. Using this insight and duality-based proof techniques from robust optimization, we reformulate the VI problem over a polyhedron as a single- level (and many-times continuously differentiable) optimization problem. This reformulation applies even if the associated cost function has an asymmetric Jacobian matrix. We give sufficient conditions for the convexity of this reformulation and thereby identify a class of VIs, of which monotone affine (and possibly asymmetric) VIs are a special case, which may be solved using widely-available and commercial-grade convex optimization software. In the second part of the thesis, we propose a distribution-free model of incomplete- information games, in which the players use a robust optimization approach to contend with payoff uncertainty.(cont.) Our "robust game" model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative, distribution-free equilibrium concept, for which, in contrast to ex post equilibria, existence is guaranteed. We show that computation of "robust-optimization equilibria" is analogous to that of Nash equilibria of complete- information games. Our results cover incomplete-information games either involving or not involving private information. In the third part of the thesis, we consider uncertainty on the part of a mechanism designer. Specifically, we present a novel, robust optimization model of the network design problem (NDP) under demand uncertainty and congestion effects, and under either system- optimal or user-optimal routing. We propose a corresponding branch and bound algorithm which comprises the first constructive use of the price of anarchy concept. In addition, we characterize conditions under which the robust NDP reduces to a less computationally demanding problem, either a nominal counterpart or a single-level quadratic optimization problem. Finally, we present a novel traffic "paradox," illustrating counterintuitive behavior of changes in cost relative to changes in demand.by Michele Leslie Aghassi.Ph.D