4 papers · 1 filter
Small lattice polytopes have few vertices
Travis Dillon
This is a geometric retelling of Konyagin and Sevast'yanov's proof of Andrew's theorem, which is a tight upper bound on the number of vertices of a d-dimensional lattice polytope i…
Closed curve covering and multiagent TSP ratios
Travis Dillon, Adrian Dumitrescu
How efficiently can a closed curve of unit length in be covered by closed curves so as to minimize the maximum length of the curves? We show that the maximum…
Quantitative selection theorems
Travis Dillon
The point selection theorem says that the convex hull of any finite point set contains a point that lies in a positive proportion of the simplices determined by that set. This pape…
Hollow polytopes with many vertices
Srinivas Arun, Travis Dillon
Given a set , a hollow polytope has vertices in but contains no other point of in its interior. We prove upper and lower bounds on the maximum num…