On The Circuit Diameters of Some Combinatorial Polytopes
MetadataShow full item record
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.
Cite this version of the work
Sean Kafer (2017). On The Circuit Diameters of Some Combinatorial Polytopes. UWSpace. http://hdl.handle.net/10012/12413
Showing items related by title, author, creator and subject.
Tam, Ricci Yik Chi (University of Waterloo, 2015-01-20)Ehrhart theory studies the behaviour of lattice points contained in dilates of lattice polytopes. We provide an introduction to Ehrhart theory. In particular, we prove Ehrhart's Theorem, Stanley Non-negativity, and ...
Webb, Kerri (University of Waterloo, 2004)A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of ...
Li, Eugene (University of Waterloo, 2014-10-08)Given an Euler-Lagrange system and a convex polytope in its output space, we design a switched feedback controller that drives the output to the polytope. On the polytope, the system output tracks assigned trajectories ...