On the Circuit Diameter of some Combinatorial Polytopes

2017/09/27 by Sean Kafer, Kanstantsin Pashkovich, Kafer, Sean +3 · 3 citations
Computer Science · Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Optimization and Control (math.OC) #Optimization and Packing Problems #Vehicle Routing Optimization Methods

paper · pdf · doi:10.48550/arxiv.1709.09642

openalex publication_date 2017/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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