Nimrod Megiddo
Algorithmica
In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem of n variables with m constraints. Smale established that for every number of constraints m, there is a constant c(m) such that the number of pivot steps of the self-dual algorithm, ρ(m, n), is less than c(m)(ln n)m(m+1). We improve upon this estimate by showing that ρ(m, n) is bounded by a function of m only. The symmetry of the function in m and n implies that ρ(m, n) is in fact bounded by a function of the smaller of m and n. © 1986 The Mathematical Programming Society, Inc.
Nimrod Megiddo
Algorithmica
Nimrod Megiddo, Dharmendra S. Modha
FAST 2003
Masakazu Kojima, Nimrod Megiddo, et al.
Operations Research Letters
Noga Alon, Nimrod Megiddo
Journal of the ACM (JACM)