Academic literature on the topic 'Network analysis (Planning) Combinatorial optimization'

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008.<br>Nemhauser,George, Committee Member ; Gu, Zonghao, Committee Member ; Ergun, Ozlem, Committee Member ; Sokol, Joel, Committee Co-Chair ; Ahmed, Shabbir, Committee Chair.

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Lee, Eva K.; Committee Member: Barnes, Earl; Committee Member: Fan, Yuhong; Committee Member: Johnson, Ellis; Committee Member: Yuan, Ming. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues.

In this dissertation we examine several discrete optimization problems through the perspectives of modeling, complexity and algorithms. We first provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables in terms of cut coefficients and volume cutoff. Under a specific probabilistic model of the problem parameters, we show that for the above measure, the probability that a split cut is better than a type 1 triangle cut is higher than the probability that a type 1 triangle cut is better than a split cut. The analysis also suggests some guidelines on when type 1 triangle cuts are likely to be more effective than split cuts and vice versa. We next study a minimum concave cost network flow problem over a grid network. We give a polytime algorithm to solve this problem when the number of echelons is fixed. We show that the problem is NP-hard when the number of echelons is an input parameter. We also extend our result to grid networks with backward and upward arcs. Our result unifies the complexity results for several models in production planning and green recycling including the lot-sizing model, and gives the first polytime algorithm for some problems whose complexities were not known before. Finally, we examine how much complexity randomness will bring to a simple combinatorial optimization problem. We study a problem called the sell or hold problem (SHP). SHP is to sell k out of n indivisible assets over two stages, with known first-stage prices and random second-stage prices, to maximize the total expected revenue. Although the deterministic version of SHP is trivial to solve, we show that SHP is NP-hard when the second-stage prices are realized as a finite set of scenarios. We show that SHP is polynomially solvable when the number of scenarios in the second stage is constant. A max{1/2,k/n}-approximation algorithm is presented for the scenario-based SHP.

Fundamental problems in graph theory are of four types existence, construction, enumeration and optimization problems. Optimization problems lie at the interface between computer science and the field of operations research and are of primary importance in decision-making. In this thesis, two optimization problems are studied: the edge-integrity of networks and the network flow problem. An implementation of the corresponding algorithms is also realized.The edge integrity of a communication network provides a way to assess the vulnerability of the network to disruption through the destruction or failure of some of its links. While the computation of the edge-integrity of graphs in general has been proven to be NPcomplete, a recently published paper was devoted to a good algorithm using a technique of edge separation sequence for computing the edge integrity of trees. The main results of this paper will be presented and an implementation of this algorithm is achieved.The network flow problem models a distribution system in which commodities are flowing through an interconnected network. The goal is to find a maximum feasible flow and its value, given the capacity constraints for each edge. The three majors algorithms for this problem (Ford -Fulkerso n, Edmonds-Karp method, MPKM algorithm) are discussed, their complexities compared and an implementation of the Ford-Fulkerson and the MPKM algorithms is presented.<br>Department of Computer Science