Del Pia and Michini recently improved the upper bound of kd due to Kleinschmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k+1)d/2, and thus reduce the gap between the lower and upper bounds. In addition, we highlight connections between Euler polytopes and a parameter studied in convex matroid optimization and strengthen the lower and upper bounds for this parameter.
Citation
AdvOL report 2015/05 McMaster University, Hamilton, Ontario, Canada