Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, December 20, 2011, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Christian Lorenz Müller

The Lovasz-Vempala algorithm for computing the volume of a convex body in O*(n4) - Theory and Implementation

Volume computation of convex bodies is a problem where randomized algorithms are provably superior to deterministic ones. In the past 20 years a series of papers appeared that reduced the complexity from O*(n23) to O*(n4). The latter bound has been achieved by an algorithm proposed by Lovasz and Vempala in 2004. The algorithm can be seen as an inverse simulated annealing algorithm that heavily relies on the fast-mixing Hit-and-Run sampling scheme. This year Lovasz and Deak presented the first implementation of the algorithm as well as a number of computational results.

In this talk I will detail the working mechanisms of the Lovasz-Vempala algorithm and explain the main computational techniques necessary to arrive at an implementable algorithm.

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