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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 ..."
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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 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 RandomFacet and RandomFacet ∗ are the same is false. We provide here simple examples that show that the expected number of steps performed by the two algorithms is not the same. 1
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 this rule, on any linear program involving n inequalities in d variables, is