Approximation algorithms for terrain guarding

We present approximation algorithms and heuristics for several variations of terrain guarding problems, where we need to guard a terrain in its entirety by a minimum number of guards. Terrain guarding has applications in telecommunications, namely in the setting up of antenna networks for wireless communication. Our approximation algorithms transform the terrain guarding instance into a MINIMUM SET COVER instance, which is then solved by the standard greedy approximation algorithm [J. Comput. System Sci. 9 (1974) 256-278]. The approximation algorithms achieve approximation ratios of 0(logn), where n is the number of vertices in the input terrain. We also briefly discuss some heuristic approaches for solving other variations of terrain guarding problems, for which no approximation algorithms are known. These heuristic approaches do not guarantee non-trivial approximation ratios but may still yield good solutions. (C) 2002 Published by Elsevier Science B.V.