dc.contributor.author Kafer, Sean dc.date.accessioned 2017-09-20 19:24:18 (GMT) dc.date.available 2017-09-20 19:24:18 (GMT) dc.date.issued 2017-09-20 dc.date.submitted 2017 dc.identifier.uri http://hdl.handle.net/10012/12413 dc.description.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 . en 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. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Circuit Diameter en dc.subject Hirsch Conjecture en dc.subject Circuit Hirsch Conjecture en dc.subject Traveling Salesman Polytope en dc.subject Matching Polytope en dc.subject Perfect Matching Polytope en dc.subject Polytope Formulations en dc.subject Fractional Stable Set Polytope en dc.subject Combinatorial Diameter en dc.subject Spanning Tree Polytope en dc.subject Matroid Polytope en dc.title On The Circuit Diameters of Some Combinatorial Polytopes en dc.type Master Thesis en dc.pending false uws-etd.degree.department Combinatorics and Optimization en uws-etd.degree.discipline Combinatorics and Optimization en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Sanità, Laura uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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