Geometric secluded paths and planar satisfiability
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We consider paths with low "exposure" to a polygonal domain, i.e., paths which are seen as little as possible; we differentiate between "integral" exposure (when we care for how long the path sees every point of the domain) and "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 connection of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.
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