One line and n points * Bernd Gärtner † Falk

We analyze a randomized pivoting process involving one line and n points in the plane. The process models the behavior of the Random-Edge simplex algorithm on simple polytopes with n facets in dimension n − 2. We obtain a tight O(log n) bound for the expected number of pivot steps. This is the first nontrivial bound for Random-Edge which goes beyond bounds for specific polytopes. The process itself can be interpreted as a simple algorithm for certain 2-variable linear programming problems, and we prove a tight Θ(n) bound for its expected runtime. c © ??? John Wiley & Sons, Inc.