Sarah Cannon Diane Souvaine Andrew Winslow Art gallery problems Art gallery problems Art gallery problems Art gallery problems Art gallery problems Art gallery problems Art gallery problems ID: 541828
Download Presentation The PPT/PDF document "Hidden Mobile Guards in Simple Polygons" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Hidden Mobile Guards in Simple Polygons
Sarah Cannon Diane Souvaine Andrew WinslowSlide2
Art gallery problemsSlide3
Art gallery problemsSlide4
Art gallery problemsSlide5
Art gallery problemsSlide6
Art gallery problemsSlide7
Art gallery problemsSlide8
Art gallery problemsSlide9
Art gallery problemsSlide10
Art gallery problems
Goal: all locations seen by some guard.Slide11
Hidden guardsSlide12
Hidden guardsSlide13
Hidden guardsSlide14
Hidden guardsSlide15
Hidden guards
Claim: This polygon does not admit a hidden guard set.
Proof: Any single guard is insufficient, any two are not hidden.Slide16
Guard varieties
Open
Closed
Edge
Diagonal
Mobile
Edge
Diagonal
MobileSlide17
Simple
Polygon classes
Starshaped
Orthogonal
MonotoneSlide18
Results for hidden guards
Do all polygons in class admit a hidden guard set? Slide19
Results for hidden guards
Do all polygons in class admit a hidden guard set? Slide20
Claim: this monotone polygon does not
admit a hidden open edge guard set. Slide21
Each ear needs an edge guard inside it.
Any ear edge guard pair can’t be augmented into a hidden guard set.
Proof:Slide22Slide23Slide24
Claim: this simple polygon does not
admit a hidden open mobile guard set.Slide25
Cases 1-3
Subcases
1a-c, 2a-c
Subcases
3a-o
Subcases
3p-u
Proof by 27
subcasesSlide26Slide27
Claim: every monotone or
starshaped polygon
admits a hidden open mobile guard set.Approach: use the set of edges of a geodesic path.Slide28
Open problem!
Results for hidden guardsSlide29