An improved and simpler analysis of shadow simplex methods, where the main algorithm requires an expected O(d2 √logn σ−2 + d5 log3/2 n) number of simplex pivots, and an improved shadow bound is obtained.Expand

A scaling invariant LLS algorithm is developed, which uses and dynamically maintains improving estimates of the circuit ratio digraph, together with a refined potential function based analysis for LLS algorithms in general.Expand

This chapter begins the smoothed analysis discussion with an analysis of the successive shortest path algorithm for the minimum-cost maximum-flow problem under objective perturbations, a classical instantiation of the shadow vertex simplex method.Expand

The results give a Gaussian analogue of the classical integrality gap result of Dyer and Frieze in the case of random packing IPs and proves that the gap between the value of the linear programming relaxation and the IP is upper bounded by $\operatorname{poly}(m)(\log n)^2 / n$.Expand

This presentation explains the excellent practical performance of the simplex method for linear programming and some of the most successful frameworks for understan...Expand

Simple iterative methods for computing approximately optimal primal and dual solutions for the problem of maximizing a linear functional over a convex set given by a separation oracle are given, based on variants of the classical Von Neumann and Frank-Wolfe algorithms.Expand

The combinatorial diameter diam(P ) of a polytope P is the maximum shortest-path distance between any pair of vertices. In this paper, we provide upper and lower bounds on the combinatorial diameter… Expand