Completely unimodal numberings of a simple polytope
Discrete Applied Mathematics
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A short proof of the d-connectedness of d-polytypes
Discrete Mathematics
A Subexponential Algorithm for Abstract Optimization Problems
SIAM Journal on Computing
Rectilinear and polygonal p-piercing and p-center problems
Proceedings of the twelfth annual symposium on Computational geometry
Linear programming, the simplex algorithm and simple polytopes
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Linear Programming - Randomization and Abstract Frameworks
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Finding the Sink Takes Some Time
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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We consider a class A of generalized linear programs on the d-cube (due to Matoušek) and prove that Kalai's subexponential simplex algorithm Random-Facet is polynomial on all actual linear programs in the class. In contrast, the subexponential analysis is known to be best possible for general instances in A. Thus, we identify a "geometric" property of linear programming that goes beyond all abstract notions previously employed in generalized linear programming frameworks, and that can be exploited by the simplex method in a nontrivial setting.