Optimising Active Ranges for Point Selection in Dynamic Maps Nadine - - PowerPoint PPT Presentation

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Optimising Active Ranges for Point Selection in Dynamic Maps Nadine - - PowerPoint PPT Presentation

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Optimising Active Ranges for Point Selection in Dynamic Maps Nadine Schwartges 1 Dennis Allerkamp 2 Jan-Henrik Haunert 1 Alexander Wolff 1 ICA Generalisation Workshop 13 1 Lehrstuhl f 2 Robert Bosch Car Multimedia GmbH ur Informatik I

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Optimising Active Ranges for Point Selection in Dynamic Maps

Nadine Schwartges1 · Dennis Allerkamp2

1Lehrstuhl f¨

ur Informatik I

2Robert Bosch Car Multimedia GmbH

ICA Generalisation Workshop ’13

Universit¨ at W¨ urzburg, Germany Hildesheim, Germany

Jan-Henrik Haunert1 · Alexander Wolff1

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SLIDE 2

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Problem

+ −

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Problem

+ − dmin

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 5

Problem

+ − dmin

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 6

Problem

+ − dmin

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 7

Problem

+ − dmin

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 8

Problem

+ − dmin

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 9

Problem

+ − dmin

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 10

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

+ − dmin

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SLIDE 11

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

+ − dmin

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SLIDE 12

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 13

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 14

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 15

Problem

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 16

Active Range Optimisation

Given: set of points P constant dmin

dmin Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 17

Active Range Optimisation

Given: set of points P constant dmin Goal:

dmin

for each p ∈ P an active range A(p), such that

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 18

Active Range Optimisation

Given: set of points P constant dmin Goal:

dmin

each pair of visible points have a distance > dmin for each p ∈ P an active range A(p), such that

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 19

Active Range Optimisation

Given: set of points P constant dmin Goal:

dmin

each pair of visible points have a distance > dmin max

p∈P |A(p)|

for each p ∈ P an active range A(p), such that

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 20

Active Range Optimisation

Given: set of points P constant dmin Goal:

dmin

each pair of visible points have a distance > dmin max

p∈P |A(p)|

in order to query selected points at run time for each p ∈ P an active range A(p), such that

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 21

Active Range Optimisation

Given: set of points P constant dmin Goal:

dmin

each pair of visible points have a distance > dmin max

p∈P |A(p)|

in order to query selected points at run time for each p ∈ P an active range A(p), such that

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

x y z

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SLIDE 22

Active Range Optimisation

constrained based

Given: set of points P constant dmin Goal:

dmin

each pair of visible points have a distance > dmin max

p∈P |A(p)|

in order to query selected points at run time

constrained-based m a p g e n e r a l i z a t i

  • n

m a p g e n e r a l i z a t i

  • n

for each p ∈ P an active range A(p), such that

( W e i b e l a n d D u t t

  • n

, 1 9 9 8 )

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

x y z

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Generalisation

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

(Burghardt et al., 2007)

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Generalisation

Legibility Preservation

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

(Burghardt et al., 2007)

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Generalisation

Legibility Preservation

ensure minimum distance maximise quantity

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

(Burghardt et al., 2007)

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SLIDE 26

Generalisation

Legibility Preservation

solution: optimise for each scale ensure minimum distance maximise quantity

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

(Burghardt et al., 2007)

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SLIDE 27

Generalisation solution: optimise for each scales

Legibility Preservation

solution: optimise for each scale ensure minimum distance maximise quantity

  • ver all

in advance

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

(Burghardt et al., 2007)

  • s # labels at scale s
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SLIDE 28

Generalisation solution: optimise for each scales

Legibility Preservation

solution: optimise for each scale ensure minimum distance maximise quantity

  • ver all

in advance

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

(Burghardt et al., 2007)

⇒ no flickering

  • s # labels at scale s
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Optimisation

Mixed-Integer Linear Program (MIP)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Optimisation

Mixed-Integer Linear Program (MIP)

  • ptimal solutions

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Optimisation

Mixed-Integer Linear Program (MIP) high computation time

  • ptimal solutions

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 32

Optimisation

Mixed-Integer Linear Program (MIP) Heuristics high computation time

  • ptimal solutions

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 33

Optimisation

Mixed-Integer Linear Program (MIP) Heuristics high computation time easy to understand near-linear running time (under reasonable assumptions)

  • ptimal solutions

hopefully nearly-optimal solutions

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Optimisation

Mixed-Integer Linear Program (MIP) Heuristics high computation time easy to understand near-linear running time (under reasonable assumptions) benchmark

  • ptimal solutions

hopefully nearly-optimal solutions

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

non-optimal heuristic! non-optimal heuristic!

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SLIDE 57

Shrinking Cones

(Been et al., 2006 / Been et al., 2010)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

non-optimal heuristic! non-optimal heuristic!

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M0)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

p q

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

p q p′ q′

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

p q p′ q′ d(pp′) d(qq′) <

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

p q p′ q′ d(pp′) d(qq′) < ⇒ stop p

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Growing Cones (M1)

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

p q p′ q′ d(pp′) d(qq′) < ⇒ stop p means: Delaunay triangulation

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

249 points unit square dmin = 0.00, 0.02, . . . , 0.40

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 95

Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 98

Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 99

Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 100

Example

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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SLIDE 101

Experiments

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

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Experiments

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

real-world data

perf . MIP22 0,85 0,90 0,95 1,00 1,05 1,10 1,15 25 50 75 100 125 150 175 200 225 249 size of point sets MIP35 ShrCones M0 M1

real-world data

size of point sets

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

10 25 50 75 100 125 150 175 200 225 249 sec MIP35 ShrCones M0 M1

log-scale!

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Experiments

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

synthetic data

size of point sets

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

10 25 50 75 100 125 150 175 200 225 249 sec MIP35 ShrCones M0 M1

synthetic data

perf . MIP22 0,85 0,90 0,95 1,00 1,05 1,10 1,15 25 50 75 100 125 150 175 200 225 249 size of point sets MIP35 ShrCones M0 M1

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SLIDE 104

Experiments

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

real-world data

perf . MIP22 0,85 0,90 0,95 1,00 1,05 1,10 1,15 25 50 75 100 125 150 175 200 225 249 size of point sets MIP35 ShrCones M0 M1

real-world data

size of point sets

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

10 25 50 75 100 125 150 175 200 225 249 sec MIP35 ShrCones M0 M1

synthetic data

size of point sets

  • 3

10

  • 2

10

  • 1

10 10

1

10

2

10

3

10

4

10

5

10 25 50 75 100 125 150 175 200 225 249 sec MIP35 ShrCones M0 M1

synthetic data

perf . MIP22 0,85 0,90 0,95 1,00 1,05 1,10 1,15 25 50 75 100 125 150 175 200 225 249 size of point sets MIP35 ShrCones M0 M1

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Summary & Conclusion

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

  • Shrinking Cones Heuristic
  • Growing Cones Heuristic

– M0 – M1

Summary

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SLIDE 106

Summary & Conclusion

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

  • Shrinking Cones Heuristic
  • Growing Cones Heuristic

– M0 – M1

  • Experiments

– fast – good performance

Summary

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SLIDE 107

Summary & Conclusion

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

  • Shrinking Cones Heuristic
  • Growing Cones Heuristic

– M0 – M1

  • Experiments

– fast – good performance

Summary Conclusion applicable for real-world instances

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SLIDE 108

Summary & Conclusion

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

  • Shrinking Cones Heuristic
  • Growing Cones Heuristic

– M0 – M1

  • Experiments

– fast – good performance

Summary Conclusion applicable for real-world instances

– thinning out points

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SLIDE 109

Summary & Conclusion

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

  • Shrinking Cones Heuristic
  • Growing Cones Heuristic

– M0 – M1

  • Experiments

– fast – good performance

Summary Conclusion applicable for real-world instances

– thinning out points – labeling with discs (POIs)

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SLIDE 110

Summary & Conclusion

Optimizing Active Ranges for Point Selection in Dynamic Maps, N. Schwartges, Univ. W¨ urzburg

  • Shrinking Cones Heuristic
  • Growing Cones Heuristic

– M0 – M1

  • Experiments

– fast – good performance

Summary Conclusion applicable for real-world instances

– thinning out points – labeling with discs (POIs)

Thank you!