1. Multicore Programming Skip list Tutorial 10 CS 0368-3469 Spring 2010

2. 2 Set Object Interface Collection of elements No duplicates Methods –add() a new element –remove() an element –contains() if element is present

3. 3 Many are Cold but Few are Frozen Typically high % of contains() calls Many fewer add() calls And even fewer remove() calls –90% contains() –9% add() –1% remove() Folklore? –Yes but probably mostly true

4. 4 Concurrent Sets Balanced Trees? –Red-Black trees, AVL trees, … Problem: no one does this well … … because rebalancing after add() or remove() is a global operation

5. 5 Skip Lists 2 2 5 5 8 8 7 7 9 9 0 0 Probabilistic Data Structure No global rebalancing Logarithmic-time search

6. 6 Skip List Property 9 9 0 0 Each layer is sublist of lower-levels

7. 7 Skip List Property 7 7 9 9 0 0 Each layer is sublist of lower-levels

8. 8 Skip List Property 5 5 7 7 9 9 0 0 Each layer is sublist of lower-levels

9. 9 Skip List Property 5 5 8 8 7 7 9 9 0 0 Each layer is sublist of lower-levels

10. 10 Skip List Property 2 2 5 5 8 8 7 7 9 9 0 0 Each layer is sublist of lower-levels Lowest level is entire list

11. 11 Skip List Property 2 2 5 5 8 8 7 7 9 9 0 0 Each layer is sublist of lower-levels Not easy to preserve in concurrent implementations …

12. 12 Search 2 2 5 5 8 8 7 7 9 9 0 0 contains(8) Too far

13. 13 Search 2 2 5 5 8 8 7 7 9 9 0 0 contains(8) OK

14. 14 Search 2 2 5 5 8 8 7 7 9 9 0 0 contains(8) Too far

15. 15 Search 2 2 5 5 8 8 7 7 9 9 0 0 contains(8) Too far

16. 16 Search 2 2 5 5 8 8 7 7 9 9 0 0 contains(8) Yes!

17. 17 7 7 Search 8 0 0 2 2 5 5 9 9 contains(8)

18. 18 7 7 Logarithmic 8 0 0 2 2 5 5 9 9 contains(8) Log N

19. 19 Why Logarthimic 2 2 5 5 8 8 7 7 9 9 0 0 Property: Each pointer at layer i jumps over roughly 2 i nodes Pick node heights randomly so property guaranteed probabilistically 2i2i 2i2i

20. 20 Find() -- Sequential int find(T x, Node [] preds, Node [] succs) { … }

21. 21 Find() -- Sequential int find(T x, Node [] preds, Node [] succs) { … } object height (-1 if not there)

22. 22 Find() -- Sequential int find(T x, Node [] preds, Node [] succs) { … } Object sought object height (-1 if not there)

23. 23 Find() -- Sequential int find(T x, Node [] preds, Node [] succs) { … } object sought return predecessors Object height (-1 if not there)

24. 24 Find() -- Sequential int find(T x, Node [] preds, Node [] succs) { … } object sought return predecessors return successors object height (-1 if not there)

25. 25 Successful Search 2 2 5 5 8 8 7 7 9 9 0 0 find(7, …) prev 0 1 2 3 4

26. 26 Successful Search 2 2 5 5 8 8 7 7 9 9 0 0 find(7, …) curr 0 1 2 3 4 prev 0 1 2 3 4

27. 27 Unsuccessful Search 2 2 5 5 8 8 7 7 9 9 0 0 find(6, …) prev 0 1 2 3 4

28. 28 Unsuccessful Search 2 2 5 5 8 8 7 7 9 9 0 0 find(6, …) curr 0 1 2 3 4 prev 0 1 2 3 4

29. 29 Lazy Skip List Mix blocking and non-blocking techniques: –Use optimistic-lazy locking for add() and remove() –Wait-free contains() Remember: typically lots of contains() calls but few add() and remove()

30. 30 Review: Lazy List Remove aa b c d

31. 31 Review: Lazy List Remove aa b c d Present in list

32. 32 Review: Lazy List Remove aa b c d Logically deleted

33. 33 Review: Lazy List Remove aa b c d Physically deleted

34. 34 Lazy Skip Lists 2 2 5 5 8 8 7 7 Use a mark bit for logical deletion 9 9 0 0 0 0 0 0 0 0

35. 35 add(6) Create node of (random) height 4 2 2 5 5 8 8 7 7 9 9 0 0 0 0 6 6

36. 36 add(6) find() predecessors 6 2 2 5 5 8 8 7 7 9 9 0 0 0 0 0 6 6

37. 37 add(6) find() predecessors Lock them 6 2 2 5 5 8 8 7 7 9 9 0 0 0 0 0 0 6 6

38. 38 add(6) find() predecessors Lock them Validate 6 2 2 5 5 8 8 7 7 9 9 0 0 0 0 0 0 6 6 Optimistic approach

39. 39 add(6) 8 8 7 7 9 9 2 2 5 5 0 0 find() predecessors Lock them Validate Splice 0 6 6 0 0 0

40. 40 add(6) find() predecessors Lock them Validate Splice Unlock 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0

41. 41 remove(6) 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 0

42. 42 remove(6) find() predecessors 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 0

43. 43 remove(6) find() predecessors Lock victim 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 0

44. 44 8 8 7 7 9 9 2 2 5 5 0 0 6 6 remove(6) find() predecessors Lock victim Set mark (if not already set) 0 0 0 0 0 Logical remove…

45. 45 8 8 7 7 9 9 2 2 5 5 0 0 6 6 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate 0 0 1 0 0 0

46. 46 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 1 0 0 0

47. 47 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 1 0 0 0

48. 48 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 1 0 0 0

49. 49 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 1 0 0 0

50. 50 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 8 8 7 7 9 9 2 2 5 5 0 0 0 0 0 0 0

51. 51 contains(8) Find() & not marked 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 0

52. 52 contains(8) 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 0 Node 6 removed while traversed

53. 53 contains(8) 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 Node removed while being traversed

54. 54 contains(8) 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 Prove: an unmarked node (like 8) remains reachable

55. 55 8 8 7 7 9 9 2 2 5 5 0 0 6 6 remove(6): Linearization Successful remove happens when bit is set 0 0 0 0 0 Logical remove…

56. 56 Add: Linearization 8 8 7 7 9 9 2 2 5 5 0 0 Successful add() at point when fully linked Add fullyLinked bit to indicate this Bit tested by contains() 0 0 6 6 0 0 0

57. 57 contains(7): Linearization 8 8 7 7 9 9 2 2 5 5 0 0 6 6 0 0 0 0 0 When fully-linked unmarked node found Pause while fullyLinked bit unset

58. 58 contains(7): Linearization 8 8 6 6 9 9 2 2 5 5 0 0 7 7 0 0 1 0 0 When do we linearize unsuccessful Search? 1 So far OK…

59. 59 contains(7): Linearization 8 8 6 6 9 9 2 2 5 5 0 0 7 7 0 0 0 0 When do we linearize unsuccessful Search? 7 7 But what if a new 7 added concurrently?

60. 60 contains(7): Linearization 8 8 6 6 9 9 2 2 5 5 0 0 7 7 0 0 0 0 When do we linearize unsuccessful Search? 1 7 7 Prove: at some point 7 was not in the skip list

61. 61 A Simple Experiment Each thread runs 1 million iterations, each either: –add() –remove() –contains() Item and method chosen in random from some distribution

62. 62 Lazy Skip List: Performance Multiprogramming search Throughput

63. 63 Lazy Skip List: Performance Multiprogramming Higher contention search Throughput

64. 64 Lazy Skip List: Performance Multiprogramming Unrealistic Contention search Throughput

65. 65 Summary Lazy Skip List –Optimistic fine-grained Locking Performs as well as the lock-free solution in common cases Simple

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