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My main area of research is the design, analysis and implementation of algorithms for solving a variety of problems from different domains. In particular, my research concerns three interrelated areas: algorithms for computational geometry, generation of combinatorial and geometric objects, and design of geometric algorithms with applications in geographic information systems and medical physics. The common theme is the investigation of efficient computation in these areas. The goals are to generate improved techniques and to characterize as well as exploit significant relationships. Under investigations are problems that have high practical relevance and at the same time raise fundamental questions. I am also interested in the implementation of geometric algorithms.
With a large group of graduate students we undertook a comprehensive research project or find novel techniques for using parallel computers to solve computationally intensive or time-sensitive problems in spatial data manipulation. A focus area of application of this research is Geographic Information Systems (GIS). Other areas of application include Medical Imagery, Treatment Planning, as well as Environmental Modeling. Our research has attracted substantial funding allowing the acquisition of parallel computers and the research support. Most recently, we have been working on privacy issues for medical data. This area is of high relvance to governments, researchers wishing to obtain patient data, and the general public (patients wishing to have their data kept private). We apply our knowledge from Computational Geometry to obtain interesting new results. We also give guarantees for privacy by applying, generalizing and obtaining novel results for differential privacy.

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