Approximation Algorithms for Combinatorial Optimization

优化问题的常见示例包括查找网络中的最短路由、管理缓存、负载平衡、调度和计算机断层扫描（CAT扫描）。 优化问题是计算机科学、工程学、运筹学、生物信息学的许多分支以及许多工业和经济环境的基础。 优化问题必须在非理想条件下解决--由于时间限制，或者由于有关问题实例的信息有限，理想解决方案不可能实现：例如，当解决方案必须随着时间的推移逐步构建时，每一步都不知道未来的约束，或者当解决方案必须由许多代理构建时，每个代理都有自己的有限视图。 本研究开发了处理这种非理想条件的方法。一个直接的影响是，重要的优化问题，可以更有效地解决在practices.The研究人员正在研究变量的设施位置，缓冲区管理的QoS网络，可重构缓存，微处理器温度管理，网络拥塞控制，计算机断层扫描，以及线性和整数线性规划。 研究人员还为解决此类问题的算法建立了统一的基础，并通过将控制理论与最坏情况分析相结合的算法开辟了新天地。 其基础是概率方法、线性规划原对偶理论和控制理论。 智力上的优点包括加深和统一对技术上强大的一类算法的理解。 这反过来又会产生更广泛的影响，使算法更容易理解，教授和扩展。 长期影响包括提高经济效率以及技术的发展和传播。

Common examples of optimization problems include finding shortest routes in networks, managing caches, load balancing, scheduling, and computer tomography (CAT scanning). Optimization problems are fundamental to computer science, many branches of engineering, operations research, bioinformatics, and in many industrial and economic settings. Optimization problems must be solved in non-ideal conditions -- when ideal solutions are not possible due to time constraints, or because information about the problem instance is limited: for example, when the solution must be built in steps over time, with each step being taken without knowledge of future constraints, or when the solution must be built by many agents each with its own limited view. This research develops methods to deal with such non-ideal conditions. An immediate impact is that important optimization problems can be more effectively solved in practice.The researchers are studying variants of facility location, buffer management in QoS networks, reconfigurable caching, microprocessor temperature management, network congestion control, computer tomography, and linear and integer-linear programming. The researchers are also building a unifying foundation for algorithms for such problems, and breaking new ground with algorithms that integrate control theory with worst-case analysis. The foundations are in probabilistic methods, linear programming primal-dual theory and control theory. The intellectual merit includes deepening and unifying the understanding of a technically formidable class of algorithms. This in turn has the broader impact of making the algorithms easier to understand, teach, and extend. Long-term impacts include increased economic efficiency and development and dispersion of technology.