dimension, allowing the application of set cover algorithms based on ε-nets whose approximation ratio is the logarithm of the optimal number of guards rather than of the number of polygon vertices. For unrestricted guards, the infinite number of potential guard positions makes the problem even more difficult. However by restricting the guards to lie on a fine grid, a more complicated logarithmic approximation algorithm can be derived under some mild extra assumptions, as shown by . However, efficient algorithms are known for finding a set of at most vertex guards, matching Chvátal's upper bound. proved that a placement for these guards may be computed in O(n log n) time in the worst case, via a divide and conquer algorithm. gave a linear time algorithm by using Fisk's short proof and Bernard Chazelle's linear time plane triangulation algorithm. For simple polygons that do not contain holes, the existence of a constant factor approximation algorithm for vertex and edge guards was conjectured by Ghosh. Ghosh's conjecture was initially shown to be true for vertex guards in two special sub-classes of simple polygons, viz. monotone polygons and polygons weakly visible from an edge. presented an approximation algorithm that computes in polynomial time a vertex guard set for a monotone polygon such that the size of the guard set is at most 30 times the optimal number of vertex guards. presented an approximation algorithm that computes in O(n2) time a vertex guard set for a simple polygon that is weakly visible from an edge such that the size of the guard set is at most 6 times the optimal number of vertex guards. Subsequently, claimed to have settled the conjecture completely by presenting constant factor approximation algorithms for guarding general simple polygons using vertex guards and edge guards. For vertex guarding the subclass of simple polygons that are weakly visible from an edge, a polynomial-time approximation scheme was proposed by . An exact algorithm was proposed by for vertex guards. The authors conducted extensive computational experiments with several classes of polygons showing that optimal solutions can be found in relatively small computation times even for instances associated to thousands of vertices. The input data and the optimal solutions for these instances are available for download. Three dimensions If a museum is represented in three dimensions as a polyhedron, then putting a guard at each vertex will not ensure that all of the museum is