AF: Small: Approximation Algorithms for Network Design

网络设计中的基本问题已经成为开发新技术和评估其在组合优化中的有效性的基准。本文将研究一类连通性问题，包括旅行商问题及其密切相关的变种，如桥连通性增强问题，两个边缘连通子图问题和顶点连通网络设计问题，以设计改进的近似算法，通过推进现有技术和开发新的方法。该建议还开发了新的理论模型，网络设计问题，从实践中纳入信息聚合的次添加剂的需求，并整合库存存储和物流规划中的车辆路径成本。由于其应用的普遍性，以及其理论的基本性质，网络设计问题在实践和理论上都很重要。开发的新方法可以被纳入实际的启发式方法，用于解决从通信到物流网络的大量应用中出现的现实规模的原型硬优化问题。发展的理论分析将提高这一类重要的计算优化问题的快速启发式解决方案的数学可证明的质量。

Fundamental problems in network design have served as benchmarks for the development of new techniques and evaluating their effectiveness in combinatorial optimization. This proposal will investigate a class of connectivity problems including the traveling salesperson problem and its closely related variants such as the bridge connectivity augmentation problem, two-edge-connected subgraph problem and vertex connectivity network design problems, in order to design improved approximation algorithms by advancing current techniques and developing new methods. The proposal also develops new theoretical models for network design problems from practice that incorporate sub-additive demands in information aggregation, and that integrate inventory storage and vehicle routing costs in logistics planning. Due to the ubiquity of their applications, and the fundamental nature of their theory, network design problems are important both in practice and theory. New methods developed can be incorporated into practical heuristic approaches for solving prototypically hard optimization problems of real-life scale that arise in a host of applications from communications to logistics networks. The theoretical analysis developed will improve the mathematically provable quality of fast heuristic solutions for this important class of computational optimization problems.