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Random-Facet and Random-Bland require subexponential time even for shortest paths

by Oliver Friedmann , Thomas Dueholm Hansen , Uri Zwick , 2014
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An improved version of the Random-Facet pivoting rule for the simplex algorithm

by Thomas Dueholm Hansen, Uri Zwick , 2015
"... The Random-Facet 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 Random-Facet 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 this rule, on any linear program involving n inequalities in d variables, is