1987
DOI: 10.1007/978-3-642-61578-8
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The Simplex Method

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Cited by 138 publications
(24 citation statements)
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“…It has been shown to give polynomial bounds for the simplex method over random and smoothed linear programs [5,19,21]. As mentioned above, Brunsch and Röglin [7] already showed that it yields short paths for the polyhedra we consider here.…”
Section: Definitionmentioning
confidence: 82%
See 1 more Smart Citation
“…It has been shown to give polynomial bounds for the simplex method over random and smoothed linear programs [5,19,21]. As mentioned above, Brunsch and Röglin [7] already showed that it yields short paths for the polyhedra we consider here.…”
Section: Definitionmentioning
confidence: 82%
“…This lemma, which was already used byin [11], implies that if P satisfies the local δ-distance property then so does F i , where the definition of local δ-distance is understood relative to the affine hull of F i , 5 because the normal vectors of F i arise from orthogonal projections of the normal vectors of P.…”
Section: Lemma 22 Let F Be a Cone Of An N-dimensional Cone Triangulatmentioning
confidence: 96%
“…See [11] for results on the simplex method. An average case analysis can lead to new methods that could not be found otherwise.…”
Section: Different Settingsmentioning
confidence: 99%
“…, b 3 = 1/2 (see [4]). Double-inequality (1.2) refines a result due to Borgwardt [10], who proved (1.2) with a 2 = 0 and b 2 = 1. An improvement of the left-hand side of (1.3) was given by Merkle [17].…”
Section: Introductionmentioning
confidence: 66%