The research centers on a class of geometric problems involving unions of objects. A variety of much-studied problems in combinatorial and computational geometry can be cast in these terms. Building on significant previous experience investigating the connections between combinatorics and algorithmics, the investigators explore combinatorial problems arising in the union-of-objects questions in order to develop new, simple, and powerful combinatorial tools and to refine those already available. Refining the techniques developed so far, the work expands the scope of problems to encompass questions of optimization in overlays of objects.
Throughout the investigation, the researchers emphasize the following theme: Developing new, more powerful tools for dealing with combinatorial problems. Discovery of easier proofs of and streamlined approaches to ``classical'' problems makes research results significantly more accessible to students and non-specialists and ultimately more relevant to its claimed beneficiaries, the practitioners in the application areas. Moreover, they are very likely to foster further progress in the field.
