In the wireless localization problem, given a polygon P ⊂ R, we have to place guards and fix their angular range such that P can be described using these guards. The guards describe P if for every point pair p ∈ P and q / ∈ P , there is a guard that sees p but does not see q. We consider the analogous problem in 3D: given a polyhedron P ⊂ R, place guards—which now are polyhedral cones—that coll...

Art gallery problems are, broadly speaking, the study of the relation between the shapes of regions in the plane and the number of points needed to guard them. These problems have been extensively studied over the last decade and have found different type of applications in practical situation. Normally the number of sides of a polygon or the general shape of the polygon is used as a measure of...

“Entry Guards” in the Tor anonymity network mitigate against several traffic analysis attacks including the “predecessor” attack, statistical profiling, and passive AS-level correlation attacks. Several recent works have shown that the current design does not provide sufficient mitigation against these attacks and may also introduce new vulnerabilities. We propose a simple response to these res...

The art gallery problem enquires about the least number of guards sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. Most standard versions of this problem are known to be NP-hard. In 1987, Ghosh provided a deterministic O(log n)approximation algorithm for the case of vertex guards and edge guards in simple polygons. In the same paper, Ghosh also conjecture...

The mechanism for picking guards in Tor suffers from security problems like guard fingerprinting and from performance issues. To address these issues, Hayes and Danezis proposed the use of guard sets, in which the Tor system groups all guards into sets, and each client picks one of these sets and uses its guards. Unfortunately, guard sets frequently need nodes added or they are broken up due to...

We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on the external walls of a dark building, in order to completely illuminate it? We consider both closed and open face guards (i.e., faces with or without their boundary), and we give some upper and lower bounds on the min...