Final Activity Report Summary - APPROXBIOGEO (Geometric approximation algorithms and applications to bioinformatics)
We designed approximation algorithms for the following geometric problems. The first problem we considered is to compute a shortest path between two points under anisotropic and non-uniform metrics. Second, we showed how to construct approximate Voronoi diagrams under doubling metrics, and how to construct approximate Voronoi cells. Then, we gave efficient approximation algorithms for matching two geometric shapes, and for fitting a histogram to a set of points. Finally, we developed a program for predicting the three-dimensional shape of a protein, given its amino-acid sequence.