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    Two New Bounds for the Random-Edge Simplex Algorithm (2005)
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    Publication Date: 2014-11-21
    Description: We prove that the Random-Edge simplex algorithm requires an expected number of at most $13n/sqrt(d)$ pivot steps on any simple d-polytope with n vertices. This is the first nontrivial upper bound for general polytopes. We also describe a refined analysis that potentially yields much better bounds for specific classes of polytopes. As one application, we show that for combinatorial d-cubes, the trivial upper bound of $2^d$ on the performance of Random-Edge can asymptotically be improved by any desired polynomial factor in d.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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