## 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: Thursday, March 29, 2007, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Yves Brise

## LP-type problems, a linear time algorithm further simplified

LP-type problems are an abstract framework that includes Linear Programming and several other geometric problems, for example Smallest Enclosing Ball. In this talk, I present a linear time, three- staged procedure that has been known for some time now. The first two stages are due to Clarkson, and the last one is due to Kalai, and to Matou\u{s}ek, Sharir, and Welzl. The combination of these three stages leads to a procedure for non-degenerate LP-type problems with at most $O(d^2 n + e^{\sqrt{d \log d}})$ arithmetic operations, where $n$ is the number of constraints and $d$ is the combinatorial dimension of the problem.

My work has been mainly concerned with the second stage, in particular the simplification of the analysis by getting rid of an artificial check, that was only part of the algorithm for analytical reasons.

Information for students and suggested topics for student talks