Research in Algorithms, Approximatiion and Applications

本研究的主要目标和智力价值是提高我们处理计算困难的优化问题的理解和能力，扩大我们的方法范围，以促进在多重标准发挥作用的多方面情况下的有效决策，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地解决它们。提出的研究的一个重点是关注多标准问题的连贯算法理论的发展。这样的问题是很常见的，到目前为止，大多是被挤进一个一维的模具。除了将开发的一般理论和算法外，数据库中涉及资源和效用交易的几个问题。我们将从这个角度来讨论S。第二个推动力涉及硬逼近问题理论的进一步发展。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，与实例的大小无关。第三个推动力涉及系统建模和分析中的问题，并寻求将相关问题公式化并带入算法分析领域。拟议的研究的更广泛的影响预计将来自于理论计算机科学的方法和工具与其他领域出现的问题和问题之间的联系。数据库和系统分析。预计这将是有益的。两边都是T。

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.