Motivated by secure wireless networking, we consider the problem of placing fixed localizers that enable mobile communication devices to prove they belong to a secure region that is defined by a simple polygon. Each localizer views an infinite wedge of the plane, and a device can prove membership in the secure region if it is inside the wedges for a set of localizers whose common intersection contains no points outside the polygon. This model leads to a broad class of new art gallery type problems, for which we provide upper and lower bounds.
(Joint work by David Eppstein, Michael T. Goodrich, and Nodari Sitchinava.)
This paper has been submitted to the Symposium on Computational Geometry (SoCG '06).