An Approximation Algorithm For Point Guard Problem

In 1973, Victor Klee posed the following question: How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This resulted in many subsequent researches so that the various versions of the art gallery problem were posed. Most of the versions posed are NP-hard, so designing approximation algorithms becomes important. The best algorithms for vertex and edge guard problems have logarithmic approximation factor, but with point guard problem, for the endlessness of search space, there has not posed any polynomial approximation algorithm as it would have some approximation factor better than     3 n and running time better than ) ( 3 n O . In this paper, a new approximation algorithm is proposed for point guard problem with     8 n approximation factor. The time complexity of the proposed algorithm