The Worst-Case Running Time of the Random Simplex Algorithm is Exponential in the Height

The random simplex algorithm for linear programming proceeds as follows: at each step, it moves from a vertex v of the polytope to a randomly chosen neighbor of v, the random choice being made from those neighbors of v that improve the objective function. We exhibit a polytope defined by n constraints in three dimensions with height O(logn), for which the expected running time of the random simplex algorithm is W(n/logn).