Algorithms for volume computation
The volume is one of the central properties of a convex body, and volume computation is involved in many hard problems. Applications range from rather classical ones as in convex optimization to problems in remote fields like algebraic geometry where the number of common roots of polynomials can be related to a special polytope volume. Part of the fascination of the subject stems from the discrepancy between the intuitive notion of "volume" and the actual hardness of computing it. Despite this discouraging complexity - algorithms in general need exponential time in the input dimension - steadily growing computer power enables us to attack problems of practical interest. Vinci is an easy to install C package that implements the state of the art algorithms for volume computation. It is the fruit of a research project carried out at the IFOR (Institute for Operations Research) at ETH Zürich, in collaboration with Benno Büeler and Komei Fukuda.