Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, April 26, 2011, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Edward D. Kim (TU Delft)

Polyhedral graph abstractions and weaker versions of the Hirsch Conjecture

Combinatorial abstractions of the graphs of polyhedra are receiving renewed interest as an approach to the Linear Hirsch and Polynomial Hirsch Conjectures, since Santos disproved the Hirsch Conjecture, which was relevant in the theoretical worst-case running time of the simplex method for linear programming. We will give a survey of some known combinatorial abstractions. Then we show how they fit into a more general framework, which leads to some variants of these earlier abstractions. This flexible framework is defined by combinatorial properties, with each collection of properties taken providing a variant for studying the diameters of polyhedral graphs. We present a variant which has superlinear diameter, which together with some combinatorial operations gives a concrete approach for disproving the Linear Hirsch Conjecture. The talk is completely self-contained and no prior knowledge is assumed.

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