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Reviewed by György Dósa (Veszprém) References

By Haim (il-tlav-sc) Katz, Matthew J. (il-bgun-c and Gila (il-bgun-c) Sharir

Abstract

Optimal cover of points by disks in a simple polygon. (English summary) SIAM J. Comput. 40 (2011), no. 6, 1647–1661.1095-7111 The paper gives a nice overview on geometric packing problems, mainly considering disc covering problems. Then the paper gives a new technique for the following problem: Given a simple polygon and a set of points in it, find a cover of the points by the minimum number of (variable-sized) disks which are in the polygon. By the new method the paper proposes an almost linear time algorithm which produces the optimal solution. After this main result some generalizations are treated as well, namely, covering by homothets and covering in an annulus

Year: 2013
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