Wireless Localization with Vertex Guards is NP-hard

We consider a special class of art gallery problems inspired by wireless localization. Given a simple polygon P, place and orient guards each of which broadcasts a unique key within a fixed angular range. In contrast to the classical art gallery setting, broadcasts are not blocked by the boundary of P. At any point in the plane one must be able to tell whether or not one is located inside P only by looking at the set of keys received. In other words, the interior of the polygon must be described by a monotone Boolean formula composed from the keys. We prove NP-hardness of several variants of the problem, in particular, for the vertex guard setting where guards must be located on vertices of P.

• Type: Journal
• Year: 2009
• Where: CCCG
• Authors: Tobias Christ, Michael Hoffmann
• Keywords: Art Gallery, Art Gallery Problems, CCCG 2009, Computational Geometry, Fixed Angular Range