几何隐蔽路与平面可满足性
Geometric secluded paths and planar satisfiability
摘要：
我们考虑具有低\emph{exposure}的路径到2D多边形域，即，尽可能少地看到路径;我们区分\emph{integral}暴露（当我们关心路径看到域中每个点的时间）和\emph{0/1}暴露（仅计算路径是否看到点）。对于积分曝光，我们给出了一个PTAS寻找域中两个给定点之间的最小曝光路径;对于0/1版本，我们证明了在一个简单的多边形中，最短路径具有最小曝光，而在域中有洞的问题变得NP-难。我们还强调了问题的最小可满足性和解决平面最小和最大SAT的变体的硬度的连接。
英文摘要：
We consider paths with low \emph{exposure} to a 2D polygonal domain, i.e., paths which are seen as little as possible; we differentiate between \emph{integral} exposure (when we care about how long the path sees every point of the domain) and \emph{0/1} exposure (just counting whether a point is seen by the path or not). For the integral exposure, we give a PTAS for finding the minimum-exposure path between two given points in the domain; for the 0/1 version, we prove that in a simple polygon the shortest path has the minimum exposure, while in domains with holes the problem becomes NP-hard. We also highlight connections of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.
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