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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