Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
414726 | Computational Geometry | 2014 | 4 Pages |
Abstract
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k)m(k) such that any m(k)m(k)-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into k coverings. As a corollary, we obtain that any m(k)m(k)-fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into k coverings. Previously only some weaker bounds were known for related problems [20].
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Balázs Keszegh, Dömötör Pálvölgyi,