Improved Bounds for Wireless Localization

We consider a novel 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. Broadcasts are not blocked by the edges of P. The interior of the polygon must be described by a monotone Boolean formula composed from the keys. We improve both upper and lower bounds for the general setting by showing that the maximum number of guards to describe any simple polygon on n vertices is between roughly 3 5 n and 4 5 n. For the natural setting where guards may be placed aligned to one edge or two consecutive edges of P only, we prove that n - 2 guards are always sufficient and sometimes necessary.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Tobias Christ, Michael Hoffmann, Yoshio Okamoto, Takeaki Uno
• Keywords: ALGORITHMICA 2010, Art Gallery Problems, Fixed Angular Range, Simple Polygon