On The Circuit Diameters of Some Combinatorial Polytopes
Abstract
The combinatorial diameter of a polytope P is the maximum value of a shortest path between two vertices of P, where the path uses the edges of P only. In contrast to the combinatorial diameter, the circuit diameter of P is defined as the maximum value of a shortest path between two vertices of P, where the path uses potential edge directions of P i.e., all edge directions that can arise by translating some of the facets of P .
In this thesis, we study the circuit diameter of polytopes corresponding to classical combinatorial optimization problems, such as the Matching polytope, the Traveling Sales man polytope and the Fractional Stable Set polytope. We also introduce the notion of the circuit diameter of a formulation of a polytope P. In this setting the circuits are determined from some external linear system describing P which may not be minimal with respect to its constraints. We use this notion to generalize other results of this thesis, as well as introduce new results about a formulation of the Spanning Tree polytope and a formulation of the Matroid polytope.
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Cite this version of the work
Sean Kafer
(2017).
On The Circuit Diameters of Some Combinatorial Polytopes. UWSpace.
http://hdl.handle.net/10012/12413
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