Concurrent Skip Lists. Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit

Transcription

1 Concurrent Skip Lists Companion slides for The by Maurice Herlihy & Nir Shavit

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

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

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 4

5 Skip Lists Probabilistic Data Structure No global rebalancing Logarithmic-time search

6 Skip List Property Each layer is sub-list of lower levels 6

7 Skip List Property Each layer is sub-list of lower-levels

8 Skip List Property Each layer is sub-list of lower levels

9 Skip List Property Each layer is sub-list of lower levels

10 Skip List Property Each layer is sub-list of lower levels Lowest level is entire list 1

11 Skip List Property Each layer is sub-list of lower levels Not easy to preserve in concurrent implementations 11

12 Search contains() Too far 1

13 Search contains() OK 13

14 Search contains() Too far 14

15 Search contains() Too far 1

16 Search contains() Yes! 16

17 Search contains() 1

18 Log N Logarithmic contains() 1

19 Why Logarthimic Property: Each pointer at layer i jumps over roughly i nodes Pick node heights randomly so property guaranteed probabilistically i i 1

20 Sequential Find int find(t x, Node<T>[] preds, Node<T>[] succs) { }

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

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

23 Sequential Find int find(t x, Node<T>[] preds, Node<T>[] succs) { } Object height (-1 if not there) object sought return predecessors 3

24 Sequential Find int find(t x, Node<T>[] preds, Node<T>[] succs) { } Object height (-1 if not there) object sought return predecessors return successors 4

25 Successful Search preds find(, ) 4 3 1

26 Successful Search preds succs find(, )

27 Unsuccessful Search preds find(6, ) 4 3 1

28 Unsuccessful Search preds succs find(6, )

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 Review: Lazy List Remove a b c d 3

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

32 Review: Lazy List Remove a b c d Logically deleted 3

33 Review: Lazy List Remove a b c d Physically deleted 33

34 Lazy Skip Lists Use a mark bit for logical deletion 34

35 add(6) Create node of (random) height 4 6 3

36 add(6) find() predecessors 6 36

37 add(6) find() predecessors Lock them 6 3

38 add(6) find() predecessors Lock them Validate Optimistic approach 6 3

39 add(6) find() predecessors Lock them Validate Splice 6 3

40 add(6) find() predecessors Lock them Validate Splice Unlock 6 4

41 remove(6) 6 41

42 find() predecessors remove(6) 6 4

43 find() predecessors Lock victim remove(6) 6 43

44 remove(6) find() predecessors Lock victim Set mark (if not already set) Logical remove 6 44

45 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate 6 1 4

46 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove

47 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 6 1 4

48 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 6 1 4

49 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove 6 1 4

50 remove(6) find() predecessors Lock victim Set mark (if not already set) Lock predecessors (ascending order) & validate Physically remove

51 find() & not marked contains() 6 1

52 contains() Node 6 removed while traversed 6

53 contains() Node removed while being traversed 6 3

54 contains() Prove: an unmarked node (like ) remains reachable 6 4

55 remove(6): Linearization Successful remove happens when bit is set Logical remove 6

56 Add: Linearization Successful add() at point when fully linked Add fullylinked bit to indicate this Bit tested by contains() 6 6

57 contains(): Linearization When fully-linked unmarked node found Pause while fullylinked bit unset 6

58 contains(): Linearization When do we linearize unsuccessful Search? So far OK 6 1 1

59 contains(): Linearization When do we linearize unsuccessful Search? But what if a new added concurrently? 6

60 contains(): Linearization When do we linearize unsuccessful Search? Prove: at some point was not in the skip list 6 1 6

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

62 Lazy Skip List: Performance Multiprogramming 6

63 Lazy Skip List: Performance Higher contention Multiprogramming 63

64 Lazy Skip List: Performance Unrealistic Contention Multiprogramming 64

65 Summary Lazy Skip List Optimistic fine-grained Locking Performs as well as the lock-free solution in common cases Simple 6

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