presented at IEEE LDAV 2017

1. Task-based Augmented Merge trees
with Fibonacci Heaps
Charles Gueunet, Kitware & UPMC
Pierre Fortin, UPMC
Julien Jomier, Kitware
Julien Tierny, CNRS-UPMC

2. Topological analysis
• Topological abstractions
• Segmentation
[Bock et al. 2017]
[Favelier et al. 2016]

3. Large data sets
● [512³]
● 2.4 GB
● Compute power through parallelism

4. Related work
• Sequential
• Augmented tree
[Carr et al. 2000]

5. Related work
• Sequential
• Augmented tree
• Monotone path
[Chiang et al. 2005]

6. Related work
• Parallel
• Partitions:
• Load imbalance
• Redundant work
Partitions
V X
X
Shared memory:
● [Pascucci04]
● [Gueunet16]
Distributed:
● [Morozov13]
● [Landge14]
V
Monotonepath

7. Related work
• Parallel
• Partitions:
• Load imbalance
• Redundant work
• Monotone path (MP):
• Not augmented
Partitions
V X
X
Shared memory:
● [Pascucci04]
● [Gueunet16]
Distributed:
● [Morozov13]
● [Landge14]
V ● [Natarajan15]
● [Maadasamy12]
● [Carr16]
Monotonepath

8. Related work
• Parallel
• Partitions:
• Load imbalance
• Redundant work
• Monotone path (MP):
• Not augmented
Partitions
V X
X
Shared memory:
● [Pascucci04]
● [Gueunet16]
Distributed:
● [Morozov13]
● [Landge14]
Us!
V ● [Natarajan15]
● [Maadasamy12]
● [Carr16]
Monotonepath

9. • A local algorithm based on Fibonacci heaps
Contributions

10. • A local algorithm based on Fibonacci heaps
• Task-based parallelism:
• Augmented merge tree
• Augmented contour tree
Contributions

11. • A local algorithm based on Fibonacci heaps
• Task-based parallelism:
• Augmented merge tree
• Augmented contour tree
• Ready to use implementation
• Generic input (VTU/VTI, 2D/3D)
• Generic output
• Open source (TTK)
Contributions

12. Preliminaries

13. Mesh
• Generic input
• Piecewise linear scalar field
• Regular grid
• Implicit triangulation (TTK)

14. • Level set
•
Scalars

15. • Level set
•
• Sublevel set
•
Scalars

16. Merge tree
• Track merge of sublevel sets CC
• 1 Arc <-> 1 CC

17. Contour tree
• Track merge of level sets CC
• 1 Arc <-> 1 CC

18. Overview
• One local growth per arc region

19. Merge tree computation
Sequential

20. Leaf search
• Extract minima (JT)

21. • Start at minima
Leaf growth

22. Saddle stopping condition
• Vertex lower than current

23. • Fibonacci heap
• Constant merge time
Merging two regions
1 2 3 4

24. Saddle growth
• New growths:
• On saddles completed

25. Saddle growth
• New growths:
• On saddles completed
• Until 1 growth remain

26. Trunk
• Monotone path until root

27. Trunk
• Monotone path until root
• Vertex to arc: using scalars

28. Trunk
• Monotone path until root
• Vertex to arc: using scalars

29. Parallel merge tree computation

30. Tasks
• Asynchronous work unit
• Dynamic load balancing
• Runtimes:
• OpenMP
• Intel TBB
• Intel Cilk Plus
[R. van der Pas, IWOMP 2009]

31. Parallel leaf search
• Local operations
• Embarrassingly parallel

32. Parallel leaf growth
• Use tasks

33. Parallel saddle stopping condition
• No change

34. • Local only
Parallel merging regions
1 2 3 4

35. Parallel trunk detect
• Atomic counter on active tasks
• Initialized: number of leaves

36. Parallel trunk process
• Chunk of vertices
• Using scalar value

37. Parallel contour tree computation

38. Post-processing
• Post-processing
• Arc: Regular vertex list

39. Post-processing
• Post-processing
• Arc: Regular vertex list
• Nodes: Report in other tree

40. Contour tree computation
• Post-processing
• Arc: Regular vertex list
• Nodes: Report in other tree
• Combination

41. Results
Intel Xeon E5-2630 v3 CPUs (2.4 GHz, 2x8 cores, 2x16 threads)
64 GB of RAM
C++ (GCC-5.4.0), VTK, OpenMP 4.0 (additional material + TTK)

42. Merge tree computation
• 512³ regular grids
Join tree
Split tree
Time in seconds

43. Join tree
Split tree
Time in seconds
Merge tree computation
• Trunk not predictable

44. Join tree
Split tree
Time in seconds
Merge tree computation
• Most time-consuming

45. Join tree
Split tree
Times in seconds
Merge tree computation
• Average speedup: 10/16

46. Detailed speedups

47. Sequential comparison
LT: Libtourtre, CF: Contour Forests, FTM: Our implementation. 256³ grid
Time in seconds

48. Parallel comparison
Time in seconds
LT: Libtourtre, CF: Contour Forests, FTM: Our implementation. 256³ grid

49. Contour tree computation
Time in seconds
• 512³ regular grids
• Average speedup 7/16
`

50. Sequential compare (CT)
Time in seconds
LT: Libtourtre, CF: Contour Forests, FTM: Our implementation. 256³ grid

51. Parallel compare (CT)
LT: Libtourtre, CF: Contour Forests, FTM: Our implementation. 256³ grid
Time in seconds

52. Limitations

53. Application

54. Application
Segmentation

55. Application
Segmentation

56. Conclusion

57. Take home message
• New algorithm:
• Fast in sequential
• Good parallel performances
• Dynamic load balancing
thanks to tasks
• No redundancy
• Augmented tree

58. Take home message
• VTK-based implementation
• Generic input
• VTU/VTI
• 2D/3D
• Generic output
• Open source (TTK)
• Ready-to-use
• New algorithm:
• Fast in sequential
• Good parallel performances
• Dynamic load balancing
thanks to tasks
• No redundancy
• Augmented tree

59. Perspective
• Improve arc growth scalability
• Parallel combination
• Improve memory usage
• Study in-situ visualization capabilities

61. Unpredictable best scheduling:
Sequentially: How to maximize trunk ?
Appendix
E
A
B
C
D
J
I
F
G
H
K
L

62. Title Annotation
• Interesting fact