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Hidden Mobile Guards in Simple Polygons
Hidden Mobile Guards in Simple Polygons

Hidden Mobile Guards in Simple Polygons - PowerPoint Presentation

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Hidden Mobile Guards in Simple Polygons - Description

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

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Presentation on theme: "Hidden Mobile Guards in Simple Polygons"— Presentation transcript

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:Slide22
Slide23
Slide24

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

subcasesSlide26
Slide27

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