An Improved Version of the Random-Facet Pivoting Rule for the Simplex Algorithm

  title={An Improved Version of the Random-Facet Pivoting Rule for the Simplex Algorithm},
  author={T. Hansen and U. Zwick},
  journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
  • T. Hansen, U. Zwick
  • Published 2015
  • Computer Science, Mathematics
  • Proceedings of the forty-seventh annual ACM symposium on Theory of Computing
The Random-Facet pivoting rule of Kalai and of Matousek, Sharir and Welzl is an elegant randomized pivoting rule for the simplex algorithm, the classical combinatorial algorithm for solving linear programs (LPs). The expected number of pivoting steps performed by the simplex algorithm when using this rule, on any linear program involving n inequalities in d variables, is 2O(√{(n-d),log({d}/{√{n-d}}},), where log n=max{1,log n}. A dual version of the algorithm performs an expected number of at… Expand
23 Citations
Random-Edge Is Slower Than Random-Facet on Abstract Cubes
An Exponential Lower Bound for Zadeh's pivot rule
A friendly smoothed analysis of the simplex method
Enumerating parametric global minimum cuts by random interleaving
  • D. Karger
  • Mathematics, Computer Science
  • STOC
  • 2016


Two New Bounds for the Random-Edge Simplex-Algorithm
A Subexponential Algorithm for Abstract Optimization Problems
A subexponential bound for linear programming
Random edge can be exponential on abstract cubes
  • J. Matousek, Tibor Szabó
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of Computer Science
  • 2004
Lower Bounds for a Subexponential Optimization Algorithm
  • J. Matousek
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 1994
An Improved Kalai-Kleitman Bound for the Diameter of a Polyhedron
  • M. Todd
  • Mathematics, Computer Science
  • SIAM J. Discret. Math.
  • 2014
A counterexample to the Hirsch conjecture
  • F. Santos
  • Mathematics, Computer Science
  • ArXiv
  • 2010
Upper bounds for the diameter and height of graphs of convex polyhedra
  • G. Kalai
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1992
A subexponential randomized simplex algorithm (extended abstract)
  • G. Kalai
  • Mathematics, Computer Science
  • STOC '92
  • 1992