Minimum Hidden Guarding of Histogram Polygons

TL;DR

This paper presents a linear-time exact algorithm for finding the minimum hidden guard set in histogram polygons under orthogonal visibility, addressing a problem known to be NP-hard in general cases.

Contribution

It introduces a novel linear-time algorithm specifically for histogram polygons, improving efficiency for this class of problems.

Findings

Linear-time algorithm for histogram polygons

Optimal hidden guard set computation

Addresses NP-hardness in general cases

Abstract

A hidden guard set $ G $ is a set of point guards in polygon $ P $ that all points of the polygon are visible from some guards in $ G $ under the constraint that no two guards may see each other. In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility. Two points $ p $ and $ q $ are orthogonally visible if the orthogonal bounding rectangle for $ p $ and $ q $ lies within $ P $. It is known that the problem is NP-hard for simple polygon with general visibility and it is true for simple orthogonal polygon. We proposed a linear time exact algorithm for finding minimum hidden guard set in histogram polygons under orthogonal visibility. In our algorithm, it is allowed that guards place everywhere in the polygon.