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...

In the Spy game, a spy is placed first at some vertex of a graph G. Then, k > 0 guards are also occupying some vertices of G. At each turn, the spy moves at speed s ≥ 2, i.e., along at most s edges and then, each guard moves at speed 1. The spy and any number of guards may occupy the same vertex. The goal of the guards is to control the spy at distance d ≥ 0, i.e., to ensure that, at every turn...

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 ...

In the area of motion planning, considerable work has been done on guarding problems, where “guards”, modelled as points, must guard a polygonal space from “intruders”. Different variants of this problem involve varying a number of factors. The guards performing the search may vary in terms of their number, their mobility, and their range of vision. The model of intruders may or may not allow t...

We study the problem of finding optimal covers of polygonal regions using multiple mobile guards. By our definition, a point is covered if, at some time, it lies within the convex hull of the guards from which it is visible. The definition captures our desire that guards both “see” and “surround” points that they cover. Guards move along continuous timeparameterized curves within a polygonal re...

BACKGROUND The participation of children and adolescents in sports, including basketball, is becoming increasingly common, and this increased involvement raises concerns about the potential risk of sports injuries. OBJECTIVE To analyze the occurrence of sports injuries among young basketball players according to their position on the court and to associate these injuries with risk factors. ...