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Algorithms for Labeling Focus Regions
Martin Fink Lehrstuhl f¨ ur Informatik I Universit¨ at W¨ urzburg
Joint work with Jan-Henrik Haunert, Andr´ e Schulz, Joachim Spoerhase, and Alexander Wolff
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Algorithms for Labeling Focus Regions Martin Fink Lehrstuhl f ur - - PowerPoint PPT Presentation
Algorithms for Labeling Focus Regions Martin Fink Lehrstuhl f ur - - PowerPoint PPT Presentation
Algorithms for Labeling Focus Regions Martin Fink Lehrstuhl f ur Informatik I Universit at W urzburg Joint work with Jan-Henrik Haunert, Andr e Schulz, Joachim Spoerhase, and Alexander Wolff 1 /14 2 /14 Paragon Restaurant &
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Tulio Daniel’s Broiler Vios Cafe Metropolitan Grill Sodo Deli Top Pot Doughnuts I Queen City Grill Paragon Restaurant & Bar Lola Maximilien Circa Waterfront Seafood Grill
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Tulio Waterfront Seafood Grill Daniel’s Broiler Vios Cafe Lola Metropolitan Grill Circa Sodo Deli Maximilien Top Pot Doughnuts I Paragon Restaurant & Bar Top Pot Doughnuts II Cascadia Restaurant Mama’s Mexican Kitchen Etta’s Queen City Grill
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Our models
free leaders
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Our models
radial leaders free leaders
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Previous Work
Excentric Labeling [Fekete and Plaisant, 1999]
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Previous Work
Excentric Labeling [Fekete and Plaisant, 1999] Boundary Labeling [Bekos et al., 2007]
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Previous Work
Excentric Labeling [Fekete and Plaisant, 1999] Necklace Maps [Speckmann and Verbeek, 2010] Boundary Labeling [Bekos et al., 2007]
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The Radial Leader Model
minimum allowed angle to avoid label collisions
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program ≥ α c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program O(n log n) time c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program weighted version: prefer higher rated points O(n log n) time c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model
minimum allowed angle to avoid label collisions maximize number of visible labels by a dynamic program weighted version: prefer higher rated points O(n log n) time O(n2) time c s1 s2 s3 s4 s5 s6 s7
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α α
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α α consider double disk D(p, q) of minimum angle α formed with p and q α p q D(p, q)
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α consider double disk D(p, q) of minimum angle α formed with p and q build arrangement of all D(·, ·) α
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α consider double disk D(p, q) of minimum angle α formed with p and q build arrangement of all D(·, ·) check for intersection (cell of depht n
2
- )
α
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α consider double disk D(p, q) of minimum angle α formed with p and q build arrangement of all D(·, ·) check for intersection (cell of depht n
2
- )
α choose center in intersection O(n4 log n) time
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α consider double disk D(p, q) of minimum angle α formed with p and q build arrangement of all D(·, ·) check for intersection (cell of depht n
2
- )
α choose center in intersection O(n4 log n) time Variants maximize labels O(n5) time
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The Radial Leader Model with Flexible Center Position
find disk that respects minimum angle α consider double disk D(p, q) of minimum angle α formed with p and q build arrangement of all D(·, ·) check for intersection (cell of depht n
2
- )
α choose center in intersection O(n4 log n) time Variants maximize labels O(n5) time maximize angle O(n6) time
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The free leader model
labels vertically distributed with unit distances
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The free leader model
labels vertically distributed with unit distances compute non-crossing leaders
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The free leader model
labels vertically distributed with unit distances compute non-crossing leaders minimize total leader length: weighted bipartite matching [Bekos et al., 2007]
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The free leader model
labels vertically distributed with unit distances compute non-crossing leaders minimize total leader length: weighted bipartite matching no crossings
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The free leader model
labels vertically distributed with unit distances compute non-crossing leaders minimize total leader length: weighted bipartite matching no crossings
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The free leader model
labels vertically distributed with unit distances compute non-crossing leaders minimize total leader length: weighted bipartite matching no crossings fast
- O(n2+ε)
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Selecting labeled sites
Tulio Daniel’s Broiler Vios Cafe Metropolitan Grill Sodo Deli Top Pot Doughnuts I Queen City Grill Paragon Restaurant & Bar Lola Maximilien Circa Waterfront Seafood Grill
not all sites can be labeled
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Selecting labeled sites
Tulio Daniel’s Broiler Vios Cafe Metropolitan Grill Sodo Deli Top Pot Doughnuts I Queen City Grill Paragon Restaurant & Bar Lola Maximilien Circa Waterfront Seafood Grill
not all sites can be labeled label good subset
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Selecting labeled sites
Tulio Daniel’s Broiler Vios Cafe Metropolitan Grill Sodo Deli Top Pot Doughnuts I Queen City Grill Paragon Restaurant & Bar Lola Maximilien Circa Waterfront Seafood Grill
not all sites can be labeled label good subset short leaders
✗
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Selecting labeled sites
Tulio Daniel’s Broiler Vios Cafe Metropolitan Grill Sodo Deli Top Pot Doughnuts I Queen City Grill Paragon Restaurant & Bar Lola Maximilien Circa Waterfront Seafood Grill
not all sites can be labeled label good subset high weight
✗
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Selecting labeled sites
Tulio Daniel’s Broiler Vios Cafe Metropolitan Grill Sodo Deli Top Pot Doughnuts I Queen City Grill Paragon Restaurant & Bar Lola Maximilien Circa Waterfront Seafood Grill
not all sites can be labeled label good subset – nice distribution – represent all sites
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Clustered Labeling
1 labeled site k unlabeled sites
Tulio Waterfront Seafood Grill Daniel’s Broiler Vios Cafe Lola Metropolitan Grill Circa Sodo Deli Maximilien Top Pot Doughnuts I Paragon Restaurant & Bar Top Pot Doughnuts II Cascadia Restaurant Mama’s Mexican Kitchen Etta’s Queen City Grill
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Clustered Labeling
1 labeled site k unlabeled sites
Tulio Waterfront Seafood Grill Daniel’s Broiler Vios Cafe Lola Metropolitan Grill Circa Sodo Deli Maximilien Top Pot Doughnuts I Paragon Restaurant & Bar Top Pot Doughnuts II Cascadia Restaurant Mama’s Mexican Kitchen Etta’s
minimize leader length + distance to attached sites
Queen City Grill
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Clustered Labeling
1 labeled site k unlabeled sites
Tulio Waterfront Seafood Grill Daniel’s Broiler Vios Cafe Lola Metropolitan Grill Circa Sodo Deli Maximilien Top Pot Doughnuts I Paragon Restaurant & Bar Top Pot Doughnuts II Cascadia Restaurant Mama’s Mexican Kitchen Etta’s
minimize leader length + distance to attached sites
Queen City Grill
Facility Location model: solved by ILP
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Clustered Labeling
1 labeled site k unlabeled sites
Tulio Waterfront Seafood Grill Daniel’s Broiler Vios Cafe Lola Metropolitan Grill Circa Sodo Deli Maximilien Top Pot Doughnuts I Paragon Restaurant & Bar Top Pot Doughnuts II Cascadia Restaurant Mama’s Mexican Kitchen Etta’s
minimize leader length + distance to attached sites
Queen City Grill
Facility Location model: solved by ILP 95 sites, 20 labels: 124s
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007]
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007]
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007]
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007]
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007] probability ≈ distanced
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007] probability ≈ distanced Clustering: assign to closest labeled site
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A Heuristic for Clustered Labeling
Randomized initialization heuristic for k-median/k-means [Arthur and Vassilvitski, 2007] probability ≈ distanced Clustering: assign to closest labeled site – much better than uniform random selection – fast
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B´ ezier Curves as Leaders
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B´ ezier Curves as Leaders
post-processing:
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B´ ezier Curves as Leaders
post-processing: leader enters label horizontally
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces)
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces) – move towards desired shape Label ri 2ri
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces) – move towards desired shape Label ri 2ri – avoid other leaders
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B´ ezier Curves as Leaders
post-processing: – (cubic) B´ ezier curves – force-directed approach gradually improve drawing according to desired changes (forces) – move towards desired shape Label ri 2ri – avoid other leaders
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Curvy Leaders in the Radial Model
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Curvy Leaders in the Radial Model
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Curvy Leaders in the Radial Model
enter radially enter radially
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Curvy Leaders in the Radial Model
move label positions on boundary improve angle
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Conclusion and Open Problems
Free leader model prefered for smaller numbers of labeled sites Radial model for many short labels
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Conclusion and Open Problems
Free leader model prefered for smaller numbers of labeled sites Radial model for many short labels Faster algorithms for finding a good center in the radial leader model?
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Conclusion and Open Problems
Free leader model prefered for smaller numbers of labeled sites Radial model for many short labels Faster algorithms for finding a good center in the radial leader model? Make interactive methods more stable during mouse movement.
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Conclusion and Open Problems
Free leader model prefered for smaller numbers of labeled sites Radial model for many short labels Faster algorithms for finding a good center in the radial leader model? Make interactive methods more stable during mouse movement. Idea: Weights changing over time