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33
An improved version of the RandomFacet pivoting rule for the simplex algorithm
, 2015
"... The RandomFacet pivoting rule of Kalai and of Matoušek, 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 th ..."
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The RandomFacet pivoting rule of Kalai and of Matoušek, 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
PIVOTING RULES FOR THE REVISED SIMPLEX ALGORITHM
, 2014
"... Abstract. Pricing is a significant step in the simplex algorithm where an improving nonbasic variable is selected in order to enter the basis. This step is crucial and can dictate the total execution time. In this paper, we perform a computational study in which the pricing operation is computed wi ..."
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with eight different pivoting rules: (i) Bland’s Rule, (ii) Dantzig’s Rule, (iii) Greatest Increment Method, (iv) Least Recently Considered Method, (v) Partial Pricing Rule, (vi) Queue Rule, (vii) Stack Rule, and (viii) Steepest Edge Rule; and incorporate them with the revised simplex algorithm. All pivoting
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 ..."
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Cited by 6 (2 self)
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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 SIMPLEX ALGORITHM ON DUAL CYCLIC 4POLYTOPES
, 2006
"... The simplex algorithm using the random edge pivotrule on any realization of a dual cyclic 4polytope with n facets does not take more than O(n) pivotsteps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show a ..."
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The simplex algorithm using the random edge pivotrule on any realization of a dual cyclic 4polytope with n facets does not take more than O(n) pivotsteps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show
Three articles on Integral Simplex Method
, 2003
"... Set partitioning is an important problem in combinatorial optimisation with applications in diverse areas such railroad crew scheduling, aircraftcrew scheduling, truck routing, political districting, switchingcircuit designing and many other schedulingtype problems. Several approaches have been ..."
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modied version of the simplex method, which he calls as Local Integral Simplex Method, in which pivot steps are made only on one entries in the simplex tableau. The method stops making further pivots when it has found a local optimum and no more improving pivots
On Gradient Simplex Methods for Linear Programs
"... Abstract. A variety of pivot column selection rules based upon the gradient criteria (including the steepest edge) have been explored to improve the efficiency of the primal simplex method. Simplexlike algorithms have been proposed imbedding the gradient direction (GD) which includes all variables ..."
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Abstract. A variety of pivot column selection rules based upon the gradient criteria (including the steepest edge) have been explored to improve the efficiency of the primal simplex method. Simplexlike algorithms have been proposed imbedding the gradient direction (GD) which includes all variables
Combinatorial Maximum Improvement Algorithm for LP and LCP
, 1995
"... this paper, we show how one can design new pivot algorithms for solving the LP and the LCP. In particular, we are interested in combinatorial pivot algorithms which solve the LP and a certain class of LCP's. Here, a pivot algorithm is called combinatorial if the pivot choice depends only on the ..."
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Cited by 1 (1 self)
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on the signs of entries of their dictionaries. The best source of combinatorial pivot algorithms is in the theory of oriented matroid (OM) programming [Bla77a, Edm94, Fuk82, FT92, LL86, Ter87, Tod85, Wan87]. The wellknown Bland's pivot rule [Bla77b] for the simplex method can be considered as a
A basisdeficiencyallowing primal PhaseI algorithm using the mostobtuseangle column rule
, 2005
"... The dual PhaseI algorithm using the mostobtuseangle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basisdeficiencyallowing context. In this paper, we establish a basisdeficiencyallowing PhaseI algorithm using the socalled mostobtuseang ..."
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Cited by 3 (0 self)
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The dual PhaseI algorithm using the mostobtuseangle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basisdeficiencyallowing context. In this paper, we establish a basisdeficiencyallowing PhaseI algorithm using the socalled most
A Computer Implementation of the PushandPull Algorithm and Its Computational Comparison With LP Simplex method
"... The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new generalpurpose solution algorithm, called PushandPull, which obviates the use of artificial variables. The algorithm consists of preliminaries for ..."
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Cited by 2 (0 self)
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the solution back to feasibility using pivoting rules similar to the dual simplex method. All phases use the usual Gauss pivoting row operation and it is shown to terminate successfully or indicates unboundedness or infeasibility of the problem. A computer implementation, which enables the user to run either
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up
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