Research in Algorithms, Approximatiion and Applications

提出的研究的主要目标和智力价值是提高我们的理解和能力，以处理计算困难的优化问题，扩大我们的方法的范围，以促进有效的决策，在多方面的情况下，多个标准发挥作用，并将其他领域的问题形式化，并使用最合适的算法工具严格解决这些问题。涉及多准则问题的一致算法理论的发展。这类问题非常常见，迄今为止大多被压缩到一维模型中。除了一般的理论和算法，将开发，从数据库中涉及的资源和效用交易的几个问题将在这一点上解决。第二个推力涉及硬逼近问题的理论的进一步发展。一个主要的目标是理解和描述困难问题可以近似的程度，特别是，哪些问题可以在一个常数因子内近似，而与实例的大小无关。第三个推力涉及系统建模和分析中的问题，并试图制定并将相关问题纳入算法分析领域。预计拟议研究的更广泛影响将是从理论计算机科学的方法和工具之间的联系，以及在其他领域出现的问题和问题，例如。数据库和系统分析。预计这对双方都有贝内。

The main goals and the intellectual merit of the proposed research are to advance our understanding and ability to deal with computationally hard optimization problems, to expand the scope of our methodologies to facilitate e.ective decision making in multifaceted situations where multiple criteria come into play, and to formalize problems from other areas and address them rigorously using the most suitable algorithmic tools.One thrust of the proposed research concerns the development of a coherent algorithmic theory for multicriteria problems. Such problems are very common and have been mostly squeezed into an one-dimensional mold so far. Besides the general theory and algorithm that will be developed, several problems from databases involving resource and utility trade-o.s will be addressed in this light.A second thrust concerns the further development of the theory of hard approximation problems. A major objective is to understand and characterize the degree to which hard problems can be approximated, in particular, which problems can be approximated within a constant factor, independent of the size of the instance.The third thrust concerns issues in modeling and analysis of systems, and seeks to formulateand bring the relevant problems within the realm of algorithmic analysis.A broader impact of the proposed research is expected to be derived from the connections thatwill be pursued between the methodologies and tools from theoretical computer science, and theproblems and issues that arise in other areas, eg. databases and system analysis. It is expectedthat this will bene.t both sides.