Art Gallery Localization

06/21/2017

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by   Prosenjit Bose, et al.

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We study the problem of placing a set T of broadcast towers in a simple polygon P in order for any point to locate itself in the interior of P. Let V(p) denote the visibility polygon of a point p, as the set of all points q ∈ P that are visible to p. For any point p ∈ P: for each tower t ∈ T ∩ V(p) the point p receives the coordinates of t and the Euclidean distance between t and p. From this information p can determine its coordinates. We show a tower-positioning algorithm that computes such a set T of size at most 2n/3, where n is the size of P. This improves the previous upper bound of 8n/9 towers. We also show that 2n/3 towers are sometimes necessary.