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 paper, we study the circuit diameter of polytopes corresponding to classical combinatorial optimization problems, such as the matching polytope, the Traveling Salesman polytope, and the fractional stable set polytope.
On the circuit diameter of some combinatorial polytopes
Sanita Laura.
2019
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 paper, we study the circuit diameter of polytopes corresponding to classical combinatorial optimization problems, such as the matching polytope, the Traveling Salesman polytope, and the fractional stable set polytope.
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