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Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons

机译:简单直线多边形中基于信标的覆盖范围的紧张界限

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摘要

We establish tight bounds for beacon-based coverage problems. In particular, we show that [n/6] beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. When P is monotone and rectilinear, we prove that this bound becomes [n+4/8]. We also present an optimal linear-time algorithm for computing the beacon kernel of P.
机译:我们建立了基于信标的覆盖问题的紧张界限。特别是,我们表明[N / 6]信标总是足够的,有时必须覆盖具有N个顶点的简单直线多边形P.当P是单调和直线的时,我们证明这界限变为[n + 4/8]。我们还提供了一种最佳的线性时间算法,用于计算P的信标内核。

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