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- W2166579778 abstract "Suppose that two members of a finite point guard set S within a polygon P must be given different colors if their visible regions overlap, and that every point in P is visible from some point in S. The chromatic art gallery problem, introduced in [7], asks for the minimum number of colors required to color any guard set (not necessarily a minimal guard set) of P. We study two related problems. First, given a polygon P and a guard set S of P, can the members of S be efficiently and optimally colored so that no two members of S that have overlapping visibility regions have the same color? Second, given a polygon P and a set of candidate guard locations N, is it possible to efficiently and optimally choose the guard set S ⊆ N that requires the minimum number of colors? We provide an algorithm that solves the first question in polynomial time, and demonstrate the NP-hardness of the second question. Both questions are motivated by common robot tasks such as mapping and surveillance." @default.
- W2166579778 created "2016-06-24" @default.
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- W2166579778 date "2011-05-01" @default.
- W2166579778 modified "2023-09-26" @default.
- W2166579778 title "How many landmark colors are needed to avoid confusion in a polygon?" @default.
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- W2166579778 doi "https://doi.org/10.1109/icra.2011.5979838" @default.
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