In this paper, we present a new algorithm for vertex guarding of a triangulated surface, which takes into account the heights of the vertices and considers the global visibility of the guards. In this algorithm, the initial surface is reduced to a collection of simple polygons and trivial triangulated surfaces. This is done by assigning guards to some vertices and removing the faces covered by ...

Guard honey bees patrol the entrance to the nest and are thought to recognise nestmates by cuticular hydrocarbons. We aimed to determine whether honey bee guards can recognise predatory common wasps Vespula vulgaris and nestmates by olfactory cues. Odours were transferred between both honey bees and wasps and the responses of guards to controlled introductions monitored. When controlling for th...

The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here the problem is extended to 3D polyhedra, with the guards now boundary segments who rotate half-planes of illumination. After carefully detailing the 3D model, several results are established. The first is a nearly di...

The art gallery problem enquires about the least number of guards that are sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. In 1998, the problems of finding the minimum number of point guards, vertex guards, and edge guards required to guard P were shown to be APX-hard by Eidenbenz, Widmayer and Stamm. In 1987, Ghosh presented approximation algorithms for...

We present two new versions of the chromatic art gallery problem that can improve upper bound of the required colors pretty well. In our version, we employ restricted angle guards so that these modern guards can visit α-degree of their surroundings. If α is between 0 and 180 degree, we demonstrate that the strong chromatic guarding number is constant. Then we use orthogonal 90-degree guards for...

We prove that [n/2J vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that l(4n 4)/13J edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ln/3J (Everett and Rivera-Campo, 1994). Since both upper bounds are based on the four color...

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 are interested in the problem of guarding simple orthogonal polygons with the minimum number of r-guards. The interior point p belongs an orthogonal polygon P is visible from r-guard g, if the minimum area rectangle contained p and q lies within P . A set of point guards in polygon P is named guard set (as denoted G) if the union of visibility areas of these point guards be equal to polygon ...

We address the question: How many edge guards are needed to guard an orthogonal polyhedron of e edges, r of which are reflex? It was previously established [3] that e/12 are sometimes necessary and e/6 always suffice. In contrast to the closed edge guards used for these bounds, we introduce a new model, open edge guards (excluding the endpoints of the edge), which we argue are in some sense mor...

This paper presents a new synthesis-based approach for writing low-level memory-safe code. Given a partial program with missing guards, our algorithm synthesizes concrete predicates to plug in for the missing guards such that all buffer accesses in the program are memory safe. Furthermore, guards synthesized by our technique are the simplest and weakest among guards that guarantee memory safety...