Covering the plane with convex polygons
Discrete & Computational Geometry
Restricted strip covering and the sensor cover problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Multiple Coverings of the Plane with Triangles
Discrete & Computational Geometry
Convex Polygons are Cover-Decomposable
Discrete & Computational Geometry
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Indecomposable Coverings with Concave Polygons
Discrete & Computational Geometry
Decomposition of Multiple Coverings into More Parts
Discrete & Computational Geometry
Octants Are Cover-Decomposable
Discrete & Computational Geometry
Coloring half-planes and bottomless rectangles
Computational Geometry: Theory and Applications
Coloring planar homothets and three-dimensional hypergraphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Coloring hypergraphs induced by dynamic point sets and bottomless rectangles
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k) such that any 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)-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].