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Hidden Mobile Guards in Simple Polygons. 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. Art gallery problems.

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hidden mobile guards in simple polygons

Hidden Mobile Guards in Simple Polygons

Sarah Cannon Diane Souvaine Andrew Winslow

slide10

Art gallery problems

Goal: all locations seen by some guard.

slide15

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

Edge

Diagonal

Mobile

Closed

Edge

Diagonal

Mobile

slide17

Polygon classes

Orthogonal

Monotone

Starshaped

Simple

slide18

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

Proof:

Each ear needs an edge guard inside it.

Any ear edge guard pair can’t be augmented into a hidden guard set.

slide24

Claim: this simple polygon does not

admit a hidden open mobile guard set.

slide25

Proof by 27 subcases

Subcases 3a-o

Subcases 3p-u

Cases 1-3

Subcases 1a-c, 2a-c

slide27

Claim: every monotone or starshaped polygon

admits a hidden open mobile guard set.

Approach: use the set of edges of a geodesic path.