1. The Power of Two in Consistent Network Updates: Hard Loop Freedom, Easy Flow Migration
Klaus-Tycho Förster and Roger Wattenhofer

2. By Xin Jin

3. By Xin Jin

4. By Xin Jin

5. By Xin Jin

6. <
By Xin Jin

7. By Xin Jin

8. By Xin Jin

9. By Xin Jin

10. By Xin Jin

11. By Xin Jin

12. By Xin Jin

13. By Xin Jin

14. By Xin Jin

15. By Xin Jin

16. “some switches can ‘straggle,’ taking substantially more time
Appears in Practice
“some switches can ‘straggle,’ taking substantially more time
than average (e.g., x) to apply an update” Jin et al., SIGCOMM 2014

17. By Xin Jin

18. “Tree Ordering”
By Xin Jin

19. “Tree Ordering”
By Xin Jin

20. “Tree Ordering”
By Xin Jin

21. “Tree Ordering”
By Xin Jin

22. Software-Defined Networking
Centralized controller updates networks rules for optimization
Controller (control plane) updates the switches/routers (data plane)

23. old network
rules
new network
rules
network updates

24. old network
rules
new network
rules
network updates

25. possible solution: be fast!
old network
rules
new network
rules
network updates
possible solution: be fast!
e.g., B4 [Jain et al., 2013]

26. possible solution: be consistent!
old network
rules
new network
rules
network updates
possible solution: be consistent!
e.g.,
per-router ordering [Vanbever et al., 2012]
two phase commit [Reitblatt et al., 2012]
SWAN [Hong et al., 2013]
Dionysus [Jin et al., 2014] ….

27. possible solution: be consistent!
old network
rules
new network
rules
network updates
possible solution: be consistent!

29. Idea: Update as many edges as you can
Dynamic Updates
Idea: Update as many edges as you can

30. Dynamic Updates a b d a b d
network updates … …

31. Dynamic Updates a b d a b d
network updates … … a b d …

32. Dynamic Updates a b d a b d
network updates … … a b d …

33. Dynamic Updates a b d a b d
network updates … … a b d …

34. Dynamic Updates a b d a b d
network updates … … a b d …

35. Dynamic Updates … … … greedy maximum updateb d a b d
network updates … … a b d …
greedy maximum update
a & b update → all others wait
2 nodes update

36. Dynamic Updates … … … … greedy maximum updateb d a b d
network updates … … a b d a b d … …
greedy maximum update
a & b update → all others wait
2 nodes update
maximal update
a waits→ all others update
all but 1 update

37. Find maximal update?
Let’s go more general

38. Find maximal update? Let’s go more general
Delete all cycles in a graph

39. Find maximal update? Let’s go more general
Delete all cycles in a graph V1 V2 V4 V3

40. Find maximal update? Let’s go more general
Delete all cycles in a graph V1 V2 V4 V3

41. Find maximal update? Let’s go more general
Delete all cycles in a graph
NP-hard to approximate
Feedback Arc Set V1 V2 V4 V3

42. Find maximal update? ≅ Let’s go more general
Delete all cycles in a graph
NP-hard to approximate
Feedback Arc Set
And it’s equivalent  d V1 V2 ≅ V4 V3 V1 V2 V3 V4

43. Find maximal update? ≅ Let’s go more general
Delete all cycles in a graph
NP-hard to approximate
Feedback Arc Set
And it’s equivalent  V2 ≅ V3 V2 V3

44. Dynamic Updates Maximize #edges updated ≈ Feedback Arc Set
Approximate within 𝑂( log 𝑛 log log 𝑛 )
Better approximation bound for Feedback Arc?
Implies better bound for #edges

45. Scheduling Updates
But how long until all edges updated?

46. Scheduling Updates But how long until all edges updated?
Ludwig et al. (2015): NP-hard for 3-schedule

47. Scheduling Updates But how long until all edges updated?
Ludwig et al. (2015): NP-hard for 3-schedule
Our result (with 2 destinations)
NP-hard for any sublinear schedule

48. Scheduling Updates
Idea: Delay updates w' d v d w

49. Scheduling Updates
Idea: Delay updates w' w' d d v v d d w w

50. Scheduling Updates
Idea: Delay updates d' w' w' d' d' d d v v d d w w

51. Scheduling Updates Idea: Delay updates d' w' w' d' d' d d,d’ v v d d w

52. Scheduling Updates Iterate over and over and over…. d' w' w' d' d' d

53. Loop Freedom Overview Maximize updated #edges per update
NP-hard
Sublinear schedule checking for 2 destinations

55. How to Move Flows? 𝒗 𝒘 𝑺𝟐 𝑻𝟐 𝑺𝟏 𝑻𝟏

56. How to Move Flows? 𝒗 𝒘 𝑺𝟐 𝑻𝟐 𝑺𝟏 𝑻𝟏

57. How to Move Flows? 𝒗 𝒘 𝑺𝟐 𝑻𝟐 𝑺𝟏 𝑻𝟏

58. How to Move Flows? 𝒗 𝒘 𝑺𝟐 𝑻𝟐 𝑺𝟏 𝑻𝟏

59. How to Move Flows? 𝒗 𝒘 𝑺𝟐 𝑻𝟐 𝑺𝟏 𝑻𝟏

60. How Hard in General w/o Splitting?
Previous work: Fastest Migration is NP-hard

61. How Hard in General w/o Splitting?
Previous work: Fastest Migration is NP-hard
Our work: Deciding is NP-hard

62. How Hard in General w/o Splitting?
Previous work: Fastest Migration is NP-hard
Our work: Deciding is NP-hard
Reduction from Partition 𝑺𝟏
𝒗11
𝒘12 𝑻𝟏 𝑺𝟏
𝒗11
𝒘12 𝑻𝟏 … … … … 𝑺𝒌
𝒗21
𝒘22 𝑻𝒌 𝑺𝒌
𝒗21
𝒘22 𝑻𝒌 𝑺𝒃 𝑻𝒃 𝑺𝒃 𝑻𝒃

63. Issues with Splitting 𝑓𝑤 𝑓𝑤 𝒗 𝒘 𝑺𝟏 𝑻𝟏

64. Issues with Splitting 𝑓𝑤 𝑓𝑤 𝒗 𝒘 𝑺𝟏 𝑻𝟏

65. Issues with Splitting 𝑓𝑤 𝑓𝑤 𝒗 𝒘 𝑺𝟏 𝑻𝟏

66. Packets bypass Waypoints!𝑓𝑤 𝑓𝑤 𝒗 𝒘 𝑺𝟏 𝑻𝟏

67. 2-Splittable Flows Keep both flow paths at the same time
Easy updates: Change 𝑓𝑤 𝑓𝑤 𝒗 𝒘 𝑺𝟏 𝑻𝟏

68. High-Level Algorithm Idea
Establish new paths at size 0

69. High-Level Algorithm Idea
Establish new paths at size 0
Only if >0 for all paths can be obtained:
Consistent migration possible

70. High-Level Algorithm Idea
Establish new paths at size 0
Only if >0 for all paths can be obtained:
Consistent migration possible
By changing allocations over multiple steps

71. High-Level Algorithm Idea
Establish new paths at size 0
Only if >0 for all paths can be obtained:
Consistent migration possible
By changing allocations over multiple steps 𝑺𝟏
𝒗11
𝒘12 𝑻𝟏 𝑺𝟏
𝒗11
𝒘12 𝑻𝟏 … … … … 𝑺𝒌
𝒗21
𝒘22 𝑻𝒌 𝑺𝒌
𝒗21
𝒘22 𝑻𝒌 𝑺𝒃 𝑻𝒃 𝑺𝒃 𝑻𝒃

72. Summary

73. The Power of Two in Consistent Network Updates: Hard Loop Freedom, Easy Flow Migration
Klaus-Tycho Förster and Roger Wattenhofer

74. “some switches can ‘straggle,’ taking substantially more time
Appears in Practice
“Data plane updates may fall behind the control plane acknowledgments and may be even reordered.” Kuzniar et al., PAM 2015
“…the inbound latency is quite variable with a […] standard deviation of 31.34ms…” He et al., SOSR 2015
“some switches can ‘straggle,’ taking substantially more time
than average (e.g., x) to apply an update” Jin et al., SIGCOMM 2014