Degree of imprecision: Geometric and algorithmic approaches

Degree of imprecision: Geometric and algorithmic approaches

We use standard results from convex geometry to obtain representations of the prior and posterior degrees of imprecision in terms of width functions and difference bodies. These representations are used to construct algorithms for the calculation of the prior and the posterior degree of imprecision. 2006 Elsevier Inc. All rights reserved.

Theoretical and Algorithmic Approaches to

Acknowledgements First and foremost, I thank my advisor, Prof. Michael Langston. I thank him for his guidance and unwavering support, and for the many, m a n y things I have learned under his advisorship. I am grateful to the Navy for the Augmentation Award for Science and Engineering Technology (AASERT), and to Prof. Langston for awarding me the privilege of being its recipient. I thank Profs....

Algorithmic Techniques for Geometric Optimization

We review the recent progress in the design of e cient algorithms for various problems in geometric optimization. The emphasis in this survey is on the techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LP-type problems and their e cient solution.

Topics in algorithmic, enumerative and geometric combinatorics

This thesis presents five papers, studying enumerative and extremal problems on combinatorial structures. The first paper studies Forman’s discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, ...

Algorithmic Applications of Low-Distortion Geometric Embeddings