Counting blanks in polygonal arrangements

Arseniy Akopyan; Erel Segal-Halevi

doi:10.1137/16M110407X

Counting blanks in polygonal arrangements

Arseniy Akopyan, Erel Segal-Halevi

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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	https://doi.org/10.1137/16M110407X
State	Published - 2018

Keywords

Cake-cutting
Convex objects
Covering
Packing
Rectilinear polygons
Redivision

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10.1137/16M110407X

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Counting blanks in polygonal arrangements

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Keywords

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