FAW 2019: Frontiers in Algorithmics pp 26-37

# Efficient Guarding of Polygons and Terrains

• Meghana M. Reddy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11458)

## Abstract

In this paper, we study the Efficient Guarding problem - a variant of the well studied Art Gallery Problem in computational geometry. A given polygon P is considered to be guarded efficiently by a guard set G if every point in P is seen by exactly one guard in G. Here we investigate the problem of efficient guarding of all the vertices of a polygon using a vertex guard set of minimum size. We prove that it is NP-complete even to check whether an efficient guard set exists for a polygon. We then give a parameterized algorithm for the efficient guarding of a 1.5 dimensional terrain, when parameterized by a structural parameter namely, the onion peeling number of the terrain i.e, the number of convex layers of the terrain. We further give polynomial time algorithms to solve the minimum efficient guarding problem for some special polygons.

## Keywords

Art Gallery Problem Efficient Guarding FPT algorithms

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