Journal of Algorithms
Information Processing Letters
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Covering grids and orthogonal polygons with periscope guards
Computational Geometry: Theory and Applications
An optimal algorithm to solve the minimum weakly cooperative guards problem for 1-spiral polygons
Information Processing Letters
Information Processing Letters
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Multiply Guarded Guards in Orthogonal Art Galleries
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
The art gallery theorem: its variations, applications and algorithmic aspects
The art gallery theorem: its variations, applications and algorithmic aspects
Art gallery theorems for guarded guards
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge
IEEE Transactions on Computers
Weakly cooperative guards in grids
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
An efficient algorithm for mobile guarded guards in simple grids
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Watchman routes for lines and segments
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Watchman routes for lines and line segments
Computational Geometry: Theory and Applications
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A grid P is a connected union of vertical and horizontal segments. A mobile guard is a guard which is allowed to move along a grid segment, thus a point x is seen by a mobile guard g if either x is on the same segment as g or x is on a grid segment crossing g. A set of mobile guards is weakly cooperative if at any point on its patrol, every guard can be seen by at least one other guard. In this paper we discuss the classes of polygon-bounded grids and simple grids for which we propose a quadratic time algorithm for solving the problem of finding the minimum weakly cooperative guard set (MinWCMG). We also provide an O(nlogn) time algorithm for the MinWCMG problem in horizontally or vertically unobstructed grids. Next, we investigate complete rectangular grids with obstacles. We show that as long as both dimensions of a grid are larger than the number of obstacles k, k+2 weakly cooperative mobile guards always suffice to cover the grid. Finally, we prove that the MinWCMG problem is NP-hard even for grids in which every segment crosses at most three other segments. Consequently, the minimum k-periscope guard problem for 2D grids is NP-hard as well, and this answers the question posed by Gewali and Ntafos [L.P. Gewali, S. Ntafos, Covering grids and orthogonal polygons with periscope guards, Computational Geometry: Theory and Applications 2 (1993) 309-334].