Results 1  10
of
22
A subexponential lower bound for the Least Recently Considered rule for solving linear programs and games
"... The simplex algorithm is among the most widely used algorithms for solving linear programs in practice. Most pivoting rules are known, however, to need an exponential number of steps to solve some linear programs. No nonpolynomial lower bounds were known, prior to this work, for Cunningham’s Least ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
The simplex algorithm is among the most widely used algorithms for solving linear programs in practice. Most pivoting rules are known, however, to need an exponential number of steps to solve some linear programs. No nonpolynomial lower bounds were known, prior to this work, for Cunningham’s Least
Errata for: A subexponential lower bound for the Random Facet algorithm for Parity Games
, 2014
"... In [Friedmann, Hansen, and Zwick (2011)] and we claimed that the expected number of pivoting steps performed by the RandomFacet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by RandomFacet∗, a variant of RandomFacet that bases i ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
its random decisions on one random permutation. We then obtained a lower bound on the expected number of pivoting steps performed by RandomFacet ∗ and claimed that the same lower bound holds also for RandomFacet. Unfortunately, the claim that the expected number of steps performed by Random
Randomized Simplex Algorithms on KleeMinty Cubes
 COMBINATORICA
, 1994
"... We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we use combinatorial models for the KleeMinty cubes [22] and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the KleeMinty cubes ..."
Abstract

Cited by 21 (6 self)
 Add to MetaCart
leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds (for the expected running time of the randomedge simplex algorithm on KleeMinty cubes) conjectured in the literature. At the same time, we establish quadratic upper bounds
Linear Programming, the Simplex Algorithm and Simple Polytopes
 Math. Programming
, 1997
"... In the first part of the paper we survey some farreaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concerning the simplex algorithm. We describe subexponential randomized pivot ru ..."
Abstract

Cited by 31 (1 self)
 Add to MetaCart
In the first part of the paper we survey some farreaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concerning the simplex algorithm. We describe subexponential randomized pivot
The Simplex Algorithm in Dimension Three
, 2004
"... We investigate the worstcase behavior of the simplex algorithm on linear programs with three variables, that is, on 3dimensional simple polytopes. Among the pivot rules that we consider, the “random edge” rule yields the best asymptotic behavior as well as the most complicated analysis. All other ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We investigate the worstcase behavior of the simplex algorithm on linear programs with three variables, that is, on 3dimensional simple polytopes. Among the pivot rules that we consider, the “random edge” rule yields the best asymptotic behavior as well as the most complicated analysis. All other
The Random Edge Rule on ThreeDimensional Linear Programs (Extended Abstract)
, 2002
"... The worstcase expected length of the path taken by the simplex algorithm with the Random Edge pivot rule on a 3dimensional linear program with n constraints is shown to be bounded by for large enough n. ..."
Abstract
 Add to MetaCart
The worstcase expected length of the path taken by the simplex algorithm with the Random Edge pivot rule on a 3dimensional linear program with n constraints is shown to be bounded by for large enough n.
A quasipolynomial bound for the diameter of graphs of polyhedra
 Bulletin Amer. Math. Soc
, 1992
"... Abstract. The diameter of the graph of a ¿dimensional polyhedron with n facets is at most ni0^d+2 Let P be a convex polyhedron. The graph of P denoted by G(P) is an abstract graph whose vertices are the extreme points of P and two vertices u and v are adjacent if the interval [v, u] is an extreme e ..."
Abstract

Cited by 59 (4 self)
 Add to MetaCart
. It is an old standing problem to determine the behavior of the function A(d, n). The value of A(d, n) is a lower bound for the number of iterations needed for Dantzig's simplex algorithm for linear programming with any pivot rule. In 1957 Hirsch conjectured [2] that A(d, n) < n d. Klee and Walkup [6
Geometric random edge
, 2014
"... We show that a variant of the randomedge pivoting rule results in a strongly polynomial time simplex algorithm for linear programs max{cTx: Ax 6 b}, whose constraint matrix A satisfies a geometric property introduced by Brunsch and Röglin: The sine of the angle of a row of A to a hyperplane spanne ..."
Abstract
 Add to MetaCart
We show that a variant of the randomedge pivoting rule results in a strongly polynomial time simplex algorithm for linear programs max{cTx: Ax 6 b}, whose constraint matrix A satisfies a geometric property introduced by Brunsch and Röglin: The sine of the angle of a row of A to a hyperplane
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
Abstract
 Add to MetaCart
This is a preliminary version of a Chapter on Algebraic Algorithms in the up
Results 1  10
of
22