Abstract
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.
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Gärtner, B. (1998). Combinatorial Linear Programming: Geometry Can Help. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_8
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DOI: https://doi.org/10.1007/3-540-49543-6_8
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