Abstract
Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks.
| Original language | English |
|---|---|
| Pages (from-to) | 2242-2257 |
| Number of pages | 16 |
| Journal | SIAM Journal on Discrete Mathematics |
| Volume | 32 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2018 Society for Industrial and Applied Mathematics.
Keywords
- Cake-cutting
- Convex objects
- Covering
- Packing
- Rectilinear polygons
- Redivision