Altitude Terrain Guarding and Guarding Uni-Monotone Polygons

03/15/2018

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by   Stephan Friedrichs, et al.

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We show that the problem of guarding an x-monotone terrain from an altitude line and the problem of guarding a uni-monotone polygon are equivalent. We present a polynomial time algorithm for both problems, and show that the cardinality of a minimum guard set and the cardinality of a maximum witness set coincide. Thus, uni-monotone polygons are perfect; this result also extends to monotone mountains.