Abstract. We prove that the Random-Edge simplex algorithm requires an expected number of at most 13n/ √ d pivot steps on any simple d-polytope with n vertices. This is the first nontrivial upper bound for general polytopes. We also describe a refined analysis that potentially yields much better bounds for specific classes of polytopes. As one application, we show that for combinatorial d-cubes, the trivial upper bound of 2 d on the performance of Random-Edge can asymptotically be improved by any desired polynomial factor in d.
Nontrivial, but exponential upper bounds for random edge are given in REF .
Two new bounds for the random-edge simplex algorithm
SIAM Journal on Discrete Mathematics 21, 178-190 (2007)
Mathematics Computer Science