Two-Guard Walkability of Simple Polygons

Optimal Algorithms for Two-Guard Walkability of Simple Polygons

A Fast Algorithm for Covering Rectangular Orthogonal Polygons with a Minimum Number of r-Stars

Introduction This paper presents an algorithm for covering orthogonal polygons with minimal number of guards. This idea examines the minimum number of guards for orthogonal simple polygons (without holes) for all scenarios and can also find a rectangular area for each guards. We consider the problem of covering orthogonal polygons with a minimum number of r-stars. In each orthogonal polygon P,...

Covering Grids and Orthogonal Polygons with Periscope Guards

Gewali, L.P. and S. Ntafos, Covering grids and orthogonal polygons with periscope guards, Computational Geometry: Theory and Applications 2 (1993) 309-334. The problem of finding minimum guard covers is NP-hard for simple polygons and open for simple orthogonal polygons. Alternative definitions of visibility have been considered for orthogonal polygons. In this paper we try to determine the com...

Minimum Hidden Guarding of Histogram Polygons

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 ...

Open Guard Edges and Edge Guards in Simple Polygons

An open edge of a simple polygon is the set of points in the relative interior of an edge. We revisit several art gallery problems, previously considered for closed edge guards, using open edge guards. A guard edge of a polygon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon admits at most one open guard edge, and give a simple new proof tha...