Asymptotic Bounds on the Combinatorial Diameter of Random Polytopes

  title={Asymptotic Bounds on the Combinatorial Diameter of Random Polytopes},
  author={Gilles Bonnet and Daniel Dadush and Uri Grupel and Sophie Huiberts and Galyna V. Livshyts},
  booktitle={International Symposium on Computational Geometry},
The combinatorial diameter diam( P ) of a polytope P is the maximum shortest path distance between any pair of vertices. In this paper, we provide upper and lower bounds on the combinatorial diameter of a random “spherical” polytope, which is tight to within one factor of dimension when the number of inequalities is large compared to the dimension. More precisely, for an n -dimensional polytope P defined by the intersection of m i.i.d. half-spaces whose normals are chosen uniformly from the… 

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