Cutting a Cake without Harming the Toppings.
Erel Segal-Halevi · arXiv (Cornell University) · 2016
On a two-dimensional cake, there are $m$ pairwise-disjoint toppings. It is required to cut the cake to $m+b$ pieces, such that each topping is entirely contained in a unique piece, and the total number of empty pieces ($b$, blanks) is minimized. The minimal number of blanks naturally depends on the geometric constraints of the cake and its pieces. The paper presents tight bounds on the number of blanks when the pieces must be connected, convex or rectangular.