4 papers
When Natural Variables Are Not Enough: Teaching Integer Programming with Sudoku
Aled Williams
Sudoku is a compact and familiar setting for teaching a surprisingly deep lesson in integer linear programming, namely that the most natural decision variables are not always enoug…
Mixed Minkowski-Covering Inequalities for Convex Bodies and Lattices
Aled Williams
In this paper we present a sharp mixed inequality relating successive minima and quotient covering radii of origin-symmetric convex bodies with respect to lattices. The inequality…
Evaluating the Sharpness and Limitations of Bounds on the Frobenius Number
Aled Williams
In this paper we study the (classical) Frobenius problem, namely the problem of finding the largest integer that cannot be represented as a nonnegative integral combination of give…
Considering a Classical Upper Bound on the Frobenius Number
Aled Williams, Daiki Haijima
In this paper we study the (classical) Frobenius problem, namely the problem of finding the largest integer that cannot be represented as a nonnegative integral combination of give…