Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports - - PowerPoint PPT Presentation

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Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports - - PowerPoint PPT Presentation

Jul 20, 2023 310 likes •918 views

Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports Ulf Regg Steve Kieffer Tim Dwyer Kim Marriott Michael Wybrow Kiel University Monash University Graph Drawing 2014 Background: Automotive Industry 2 Background:

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SLIDE 1

Stress-Minimizing Orthogonal Layout

  • f Data Flow Diagrams with Ports

Ulf Rüegg Kiel University Steve Kieffer Tim Dwyer Kim Marriott Michael Wybrow Monash University

Graph Drawing 2014

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SLIDE 2

Background: Automotive Industry

2

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SLIDE 3

Background: Automotive Industry

2

ATOMIC NODES

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SLIDE 4

Background: Automotive Industry

2

ATOMIC NODES ORTHOGONAL EDGES

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SLIDE 5

Background: Automotive Industry

2

PORTS ATOMIC NODES ORTHOGONAL EDGES

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SLIDE 6

Background: Automotive Industry

2

PORTS ATOMIC NODES COMPOUND NODES ORTHOGONAL EDGES

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SLIDE 7

Background: Automotive Industry

2

PORTS ATOMIC NODES COMPOUND NODES ORTHOGONAL EDGES HIERARCHICAL PORTS

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SLIDE 8

Layout Requirements

3

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SLIDE 9

Layout Requirements

3

R1

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SLIDE 10

Layout Requirements

3

R1 R2

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SLIDE 11

Layout Requirements

3

R1 R3 R2

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SLIDE 12

Layout Requirements

3

R1 R3 R2

R4

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SLIDE 13

Layout Requirements

3

R1 R3 R2

R4 R5

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SLIDE 14

Layout Requirements

3

R1 R3 R2

R6 R4 R5

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SLIDE 15

Current Layout Approach

  • Use layer-based methods [Sugiyama et al. 81]

– A lot of modifications (ports etc.) [Schulze et al. 14]

4

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SLIDE 16

Current Layout Approach

  • Use layer-based methods [Sugiyama et al. 81]

– A lot of modifications (ports etc.) [Schulze et al. 14]

  • Feedback from industrial users

4

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SLIDE 17

Current Layout Approach

  • Use layer-based methods [Sugiyama et al. 81]

– A lot of modifications (ports etc.) [Schulze et al. 14]

  • Feedback from industrial users

– In general satisfying layouts

4

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SLIDE 18

Current Layout Approach

  • Use layer-based methods [Sugiyama et al. 81]

– A lot of modifications (ports etc.) [Schulze et al. 14]

  • Feedback from industrial users

– In general satisfying layouts – "Too much whitespace"

4

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SLIDE 19

Current Layout Approach

  • Use layer-based methods [Sugiyama et al. 81]

– A lot of modifications (ports etc.) [Schulze et al. 14]

  • Feedback from industrial users

– In general satisfying layouts – "Too much whitespace" – "Edge crossings not always important"

4

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SLIDE 20

Current Layout Approach

  • Use layer-based methods [Sugiyama et al. 81]

– A lot of modifications (ports etc.) [Schulze et al. 14]

  • Feedback from industrial users

– In general satisfying layouts – "Too much whitespace" – "Edge crossings not always important"

  • Desired: simple/flexible solution

4

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SLIDE 21

New Approach

  • Constrained stress minimizing layout

5

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SLIDE 22

New Approach

  • Constrained stress minimizing layout

– Similar to force-directed approaches

5

cola.js

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SLIDE 23

New Approach

  • Constrained stress minimizing layout

– Similar to force-directed approaches – Minimizes a single goal function

5

cola.js

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SLIDE 24

New Approach

  • Constrained stress minimizing layout

– Similar to force-directed approaches – Minimizes a single goal function – Subject to separation constraints

5

cola.js

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SLIDE 25

Goal Function: P-Stress

subject to certain constraints Minimize

𝑥𝑣𝑤 𝑚𝑞𝑣𝑤 − 𝑐(𝑣, 𝑤) + 2 + 𝑚−2 𝑐 𝑣, 𝑤 − 𝑚 + 2

(𝑣,𝑤)∈𝐹 𝑣<𝑤∈𝑊

6

[Dwyer et al. GD'09]

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Goal Function: P-Stress

subject to certain constraints Minimize

𝑐 𝑣, 𝑤 euclidean distance between u and v 𝑞𝑣𝑤 number of edges on shortest path between u and v 𝑚 an ideal edge length 𝑥𝑣𝑤 normalization factor (𝑨)+ max(0,𝑨)

𝑥𝑣𝑤 𝑚𝑞𝑣𝑤 − 𝑐(𝑣, 𝑤) + 2 + 𝑚−2 𝑐 𝑣, 𝑤 − 𝑚 + 2

(𝑣,𝑤)∈𝐹 𝑣<𝑤∈𝑊

repulsive attractive

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INTUITION

  • Nodes repulse each other up to a

certain distance

  • Edges contract until (individual)

ideal length is reached

[Dwyer et al. GD'09]

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SLIDE 27

R1 - Flow Constraints

7

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SLIDE 28

R1 - Flow Constraints

𝑦𝑡 + δ𝑦𝑡𝑢 ≤ 𝑦𝑢

7

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SLIDE 29

R2 - Port Constraints

FIXED POSITION

8

Port Dummy

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R2 - Port Constraints

𝑦𝑞 + δ𝑦 = 𝑦𝑜

FIXED POSITION

𝑧𝑞 − δ𝑧 = 𝑧𝑜

8

Port Dummy

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SLIDE 31

R2 - Port Constraints

𝑦𝑞 + δ𝑦 = 𝑦𝑜

FIXED POSITION

𝑧𝑞 − δ𝑧 = 𝑧𝑜

FIXED SIDE

8

Port Dummy

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R2 - Port Constraints

𝑦𝑞 + δ𝑦 = 𝑦𝑜

FIXED POSITION

𝑧𝑞 − δ𝑧 = 𝑧𝑜

FIXED SIDE

𝑦𝑞 + δ𝑦 = 𝑦𝑜

8

Port Dummy

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R2 - Port Constraints

𝑦𝑞 + δ𝑦 = 𝑦𝑜

FIXED POSITION

𝑧𝑞 − δ𝑧 = 𝑧𝑜 𝑧𝑞 + ℎ𝑜 2 ≥ 𝑧𝑜 𝑧𝑞 − ℎ𝑜 2 ≤ 𝑧𝑜

FIXED SIDE

𝑦𝑞 + δ𝑦 = 𝑦𝑜

8

Port Dummy

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R3 - Orthogonalizing Constraints

fixed

9

[Kieffer et al. GD'13]

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SLIDE 35

R3 - Orthogonalizing Constraints

𝑧𝑏 = 𝑧𝑑

9

[Kieffer et al. GD'13]

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R3 - Orthogonalizing Constraints

𝑧𝑏 = 𝑧𝑑

9

[Kieffer et al. GD'13]

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R3 - Orthogonalizing Constraints

𝑧𝑏 = 𝑧𝑑 𝑧𝑐 = 𝑧𝑑′

9

[Kieffer et al. GD'13]

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SLIDE 38

Example

10

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Example

10

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Example

10

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Example

10

[Wybrow et al. GD'10]

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Results

11

Compared to current approach (KLay Layered)

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SLIDE 43

Results

Stress

11

Compared to current approach (KLay Layered)

BETTER

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SLIDE 44

Results

Stress Average edge length

11

Compared to current approach (KLay Layered)

BETTER

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SLIDE 45

Results

Stress Average edge length Edge length variance

11

Compared to current approach (KLay Layered)

BETTER

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SLIDE 46

Results

Stress Average edge length Edge length variance Area and aspect ratio

11

Compared to current approach (KLay Layered)

BETTER

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SLIDE 47

Results

Stress Average edge length Edge length variance Area and aspect ratio Symmetry

11

Compared to current approach (KLay Layered)

BETTER

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SLIDE 48

Results

Stress Average edge length Edge length variance Area and aspect ratio Symmetry Implementation complexity

11

Compared to current approach (KLay Layered)

BETTER

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SLIDE 49

Results

Stress Average edge length Edge length variance Area and aspect ratio Symmetry Implementation complexity Edge crossings

11

Compared to current approach (KLay Layered)

BETTER WORSE

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SLIDE 50

Results

Stress Average edge length Edge length variance Area and aspect ratio Symmetry Implementation complexity Edge crossings Edge bends

11

Compared to current approach (KLay Layered)

BETTER WORSE

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SLIDE 51

Results

Stress Average edge length Edge length variance Area and aspect ratio Symmetry Implementation complexity Edge crossings Edge bends Execution time

11

Compared to current approach (KLay Layered)

BETTER WORSE

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SLIDE 52

R4/R5 - Compound Graphs

12

KLay Layered

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R4/R5 - Compound Graphs

12

CoDaFlow

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Summary - CoDaFlow

  • One goal function: minimize stress

13

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Summary - CoDaFlow

  • One goal function: minimize stress
  • Incrementally add constraints

1. No constraints 2. + Flow constraints 3. + Port costraints 4. + Non-overlap constraints 5. + Orthogonalizing constraints

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Summary - CoDaFlow

  • One goal function: minimize stress
  • Incrementally add constraints

1. No constraints 2. + Flow constraints 3. + Port costraints 4. + Non-overlap constraints 5. + Orthogonalizing constraints

  • Orthogonal edge routing with given

node positions

13

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SLIDE 57

Closer to Industrial Scale

14

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Closer to Industrial Scale

14

Thank you! Questions?

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SLIDE 59

References

  • Schulze, C. D., Spönemann, M., & von Hanxleden, R. (2014). Drawing

layered graphs with port constraints. Journal of Visual Languages & Computing.

  • Dwyer, T., Koren, Y., & Marriott, K. (2006). IPSep-CoLa: An incremental

procedure for separation constraint layout of graphs. IEEE Transactions on Visualization and Computer Graphics

  • Dwyer, T., Marriott, K., & Wybrow, M. (2009). Topology preserving

constrained graph layout. Graph Drawing.

  • Kieffer, S., Dwyer, T., Marriott, K., & Wybrow, M. (2013). Incremental

grid-like layout using soft and hard constraints. Graph Drawing.

  • Wybrow, M., Marriott, K., & Stuckey, P. (2010). Orthogonal connector
  • routing. Graph Drawing.

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