Article ID Journal Published Year Pages File Type
414726 Computational Geometry 2014 4 Pages PDF
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
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