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Hidden Mobile Guards in Simple Polygons [article]

Sarah Cannon, Diane L. Souvaine, Andrew Winslow
2012 arXiv   pre-print
We consider guarding classes of simple polygons using mobile guards (polygon edges and diagonals) under the constraint that no two guards may see each other.  ...  For instance, every monotone or starshaped polygon can be guarded using hidden open mobile (edge or diagonal) guards, but not necessarily with hidden open edge or hidden open diagonal guards.  ...  Acknowledgements We thank Csaba Tóth for helpful discussions and Richard Pollack, Joseph Malkevitch, John Iacono, and Bill Hall for suggesting interesting problems in this area.  ... 
arXiv:1206.1803v1 fatcat:6kkb2nalajaprhnmy3265dhopy

Minimum Hidden Guarding of Histogram Polygons [article]

Hamid Hoorfar, Alireza Bagheri
2017 arXiv   pre-print
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.  ...  or star-shaped polygon can be guarded using hidden open mobile (edge or diagonal) guards, but not necessarily with hidden open edge or hidden open diagonal guards.  ... 
arXiv:1708.05815v1 fatcat:6kfnjzvfk5cmbjab6fprdwtbhm

Some Results on Open-Edge and Open Mobile Guarding of Polygons and Triangulations

A. L. Bajuelos, S. Canales, G. Hernandez, M. Martins, I. Matos
2014 Computer journal  
This paper studies the number of guards that are sufficient and sometimes necessary to guard some classes of simple polygons for both open edge and open mobile guards.  ...  A mobile guard can be placed on edges and diagonals of a polygon, and the "open" prefix means that the endpoints of such edge or diagonal are not taken into account for visibility purposes.  ...  There is no open mobile guard that can see two of the points "hidden" inside the spikes.  ... 
doi:10.1093/comjnl/bxt151 fatcat:uejbfe6hjzdtbidxbsaa27wsha

Some Results on Open Edge and Open Mobile Guarding of Polygons and Triangulations [article]

Antonio Leslie Bajuelos, Santiago Canales, Gregorio Hernández, Mafalda Martins, Inês Matos
2013 arXiv   pre-print
This paper studies the number of guards that are sufficient and sometimes necessary to guard some classes of simple polygons for both open edge and open mobile guards.  ...  A mobile guard can be placed on edges and diagonals of a polygon, and the "open" prefix means that the endpoints of such edge or diagonal are not taken into account for visibility purposes.  ...  There is no open mobile guard that can see two of the points "hidden" inside the spikes.  ... 
arXiv:1306.4359v1 fatcat:3xwlpwswvzcmfntmpdpovb33zi

Open Guard Edges and Edge Guards in Simple Polygons [chapter]

Csaba D. Tóth, Godfried T. Toussaint, Andrew Winslow
2012 Lecture Notes in Computer Science  
An open edge of a simple polygon is the set of points in the relative interior of an edge.  ...  We characterize open guard edges, and derive an algorithm that finds all open guard edges of a simple n-gon in O(n) time in the RAM model of computation.  ...  For a set S ⊆ P of multiple guards, or the trajectories of mobile guards, we adopt the notion of weak visibility [2] .  ... 
doi:10.1007/978-3-642-34191-5_5 fatcat:jiw37p64hnah5i6duxmi77all4

Multi-guard covers for polygonal regions

Zohreh Jabbari, William S. Evans, David G. Kirkpatrick
2010 Canadian Conference on Computational Geometry  
We study the problem of finding optimal covers of polygonal regions using multiple mobile guards.  ...  We show, however, that every optimal three-guard boundary cover is simple (i.e., guard paths do not cross one another).  ...  Introduction Given a polygon P , we consider the problem of finding mobile guard paths of minimum total length to cover P .  ... 
dblp:conf/cccg/JabbariEK10 fatcat:37klzet5l5ct3imul63bvhgboi

On Guarding Orthogonal Polygons with Sliding Cameras [article]

Therese Biedl, Timothy M. Chan, Stephanie Lee, Saeed Mehrabi, Fabrizio Montecchiani, Hamideh Vosoughpour
2016 arXiv   pre-print
A sliding camera inside an orthogonal polygon P is a point guard that travels back and forth along an orthogonal line segment γ in P.  ...  Next, we show that the sliding guards problem is linear-time solvable if the (suitably defined) dual graph of the polygon has bounded treewidth.  ...  Finding the minimum number of guards is NP-hard on simple polygons [22] , even on simple orthogonal polygons [28] or monotone polygons [21] .  ... 
arXiv:1604.07099v1 fatcat:45wwxekczzdfvorx5bziefv6lm

A Gradient Search Algorithm for the Maximal Visible Area Polygon Problem

Helman I. Stern, Moshe Zofi
2015 American Journal of Operations Research  
This paper provides a gradient search algorithm for finding the maximal visible area polygon (VAP) viewed by an interior point in a simple polygon P .  ...  Our maximal VAP algorithm converges in a finite number of steps, and is polynomial with a complexity of ( ) 2 2 O r n , for a simple polygon P with n vertices, and r reflex vertices.  ...  Such a path may be used to guide a mobile search robot in an enclosed 2D area.  ... 
doi:10.4236/ajor.2015.53013 fatcat:kel2lmkrjbef5pcnnwipkvvipu

Guarding Path Polygons with Orthogonal Visibility [article]

Hamid Hoorfar, Alireza Bagheri
2017 arXiv   pre-print
We are interested in the problem of guarding simple orthogonal polygons with the minimum number of r -guards.  ...  The problem of finding minimum number of guards for simple polygon with general visibility is NP-hard, even if polygon be orthogonal.  ...  So, If a hidden set is also a guard set, it is called hidden guard set.  ... 
arXiv:1709.01569v1 fatcat:wmw3rmjjvjfvvchgf6zwmu5s6i

On conflict-free chromatic guarding of simple polygons [article]

Onur Çağırıcı and Subir Kumar Ghosh and Petr Hliněný and Bodhayan Roy
2020 arXiv   pre-print
We first study the scenario in which viewers can be all points of the polygon (such as a mobile robot which moves in the interior of the polygon).  ...  We show a lower bound of 3 colours in the general case of simple polygons and conjecture that this is tight. We also prove that already deciding whether 1 or 2 colours are enough is NP-complete.  ...  Consequently, the guards placed at d 1 and d 2 must be of different colours (red and blue); otherwise, say for two red guards at d 1 , d 2 , each of the 8 vertices in A would have to be guarded by a blue  ... 
arXiv:1904.08624v3 fatcat:i5kh5en7src2zhdr7ulic5gcc4

Fault tolerant mobility planning for rapidly deployable wireless networks [chapter]

Charles Shields, Vikas Jain, Simeon Ntafos, Ravi Prakash, S. Venkatesan
1998 Lecture Notes in Computer Science  
In ad-hoc networks all nodes are presumed mobile, all links are wireless, and it is in general assumed that all nodes have similar capabilities with respect to energy supply, bu ering capacity, processing  ...  RDNs can be useful in several key environments. For example, in battleeld situations a network might h a ve to be deployed in an area of variable and ?  ...  This problem asks for the minimal number of guards that need to be placed in a polygon so that each p o i n t in the polygon is visible to at least one guard.  ... 
doi:10.1007/3-540-64359-1_741 fatcat:bisras264rhmxacgaqf4mznpp4

Hide-and-Seek: Algorithms for Polygon Walk Problems [chapter]

Atlas F. Cook, Chenglin Fan, Jun Luo
2011 Lecture Notes in Computer Science  
Jack and Jill want to play hide-and-seek on the boundary of a simple polygon.  ...  This structure has additional applications for any polygon walk problem where one entity wishes to remain hidden throughout a traversal of some path.  ...  [3] sweep a polygonal chain of guards along the boundary of a simple polygon in O(n 3 ) time.  ... 
doi:10.1007/978-3-642-20877-5_48 fatcat:qeajuyg3pbdqrn7oe7mqwrkkua

A simple proof for visibility paths in simple polygons [article]

Mohammad Reza Zarrabi, Nasrollah Moghaddam Charkari
2020 arXiv   pre-print
The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons.  ...  A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path.  ...  Usually, a mobile guard is defined as a moving point inside a simple polygon P that sees in any direction for any distance.  ... 
arXiv:2004.02227v3 fatcat:oprwvnyllraediangccf4d62ze

Dynamic Guard Patrol in Stealth Games

Wael Al Enezi, Clark Verbrugge
2020 Artificial Intelligence and Interactive Digital Entertainment Conference  
Automated patrol route construction, however, is difficult, as simple approaches based on randomized movement or goal selection tend to result in unrealistic and overly repetitive guarding motion, and  ...  Guard patrols are common in stealth games, both for a sense of realism and to form a basic challenge to acting out covert behaviour.  ...  Mobile guards have been considered as an extension to this base problem, and is sometimes referred to as the Watchmen Route Problem (WRP).  ... 
dblp:conf/aiide/EneziV20 fatcat:rimj5ehmrvcenb77ouzj7xurtm

Searching with an autonomous robot

Sandor Fekete, Rolf Klein, Andreas Nuechter
2004 Proceedings of the twentieth annual symposium on Computational geometry - SCG '04  
In particular, we discuss the problem of developing a good online strategy for an autonomous mobile robot to locate an object that is hidden behind a corner or door.  ...  The watchman problem asks for a short tour along which one mobile guard can see the entire region.  ... 
doi:10.1145/997817.997885 dblp:conf/compgeom/FeketeKN04 fatcat:attbmrtninemnmzqpmk4tkaklq
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