A Constant-Factor Approximation Algorithm for Optimal 1.5D Terrain Guarding

Authors:
Boaz Ben-Moshe;Matthew J. Katz;Joseph S. B. Mitchell
Affiliations:
-;-;-
Venue:
SIAM Journal on Computing
Year:
2007

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Abstract

We present the first constant-factor approximation algorithm for a nontrivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an $O(1)$-approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor approximations follow from set cover results, our new results exploit the geometric structure of terrains to obtain a substantially improved approximation algorithm.