Research in Algorithms, Approximatiion and Applications

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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.