Approximation algorithms for art gallery problems in polygons

Abstract

In this paper, we present approximation algorithms for minimum vertex and edge guard problems for polygons with or without holes with a total of n vertices. For simple polygons, approximation algorithms for both problems run in O ( n 4 ) time and yield solutions that can be at most O ( log n ) times the optimal solution. For polygons with holes, approximation algorithms for both problems give the same approximation ratio of O ( log n ) , but the running time of the algorithms increases by a factor of n to O ( n 5 ) .