1. Fast and Lock-Free Concurrent Priority Queues for Multi-Thread Systems Håkan Sundell Philippas Tsigas

2. Outline Synchronization Methods Priority Queues Concurrent Priority Queues Lock-Free Algorithm: Problems and Solutions Experiments Conclusions

3. Synchronization Shared data structures needs synchronization Synchronization using Locks Mutually exclusive access to whole or parts of the data structure P1 P2 P3 P1 P2 P3

4. Blocking Synchronization Drawbacks Blocking Priority Inversion Risk of deadlock Locks: Semaphores, spinning, disabling interrupts etc. Reduced efficiency because of reduced parallelism

5. Non-blocking Synchronization Lock-Free Synchronization Optimistic approach Assumes its alone and prepares operation which later takes place (unless interfered) in one atomic step, using hardware atomic primitives Interference is detected via shared memory and the atomic primitives Retries until not interfered by other operations Can cause starvation

6. Non-blocking Synchronization Lock-Free Synchronization Avoids problems with locks Simple algorithms Fast when having low contention Wait-Free Synchronization Always finishes in a finite number of its own steps. Complex algorithms Memory consuming Less efficient in average than lock-free

7. Priority Queues Fundamental data structure Works on a set of pairs Two basic operations: Insert(v,p): Adds a new element to the priority queue v=DeleteMin(): Removes the element with the highest priority

8. Sequential Priority Queues All implementations involves search phase in either Insert or DeleteMin Arrays. Maximum complexity O(N) Ordered Lists. O(N) Trees. O(log N) Heaps. O(log N) Advanced structures (i.e. combinations)

9. Randomized Algorithm: Skip Lists William Pugh: Skip Lists: A Probabilistic Alternative to Balanced Trees, 1990 Layers of ordered lists with different densities, achieves a tree-like behavior Time complexity: O(log 2 N) – probabilistic! 1234567 HeadTail 50% 25% …

10. Why Skip Lists for Concurrent Priority Queues? Ordered Lists is simpler than Trees Easier to make efficient concurrently Search complexity is important Skip Lists is an alternative to Trees Lotan and Shavit: Skiplist-Based Concurrent Priority Queues, 2000 Implementation using multiple locks 1234567 L L LL L LL L L LL L LL LLLLLLL

11. Our Lock-Free Concurrent Skip List Define node state to depend on the insertion status at lowest level as well as a deletion flag Insert from lowest level going upwards Set deletion flag. Delete from highest level going downwards 1234567 DDDDDDD 1 2 3 p 1 2 3 p D

12. Overlapping operations on shared data Example: Insert operation - which of 2 or 3 gets inserted? Solution: Compare-And-Swap atomic primitive: CAS(p:pointer to word, old:word, new:word):boolean atomic do if *p = old then *p := new; return true; else return false; 1 2 3 4 Insert 3 Insert 2

13. Dynamic Memory Management Problem: System memory allocation functionality is blocking! Solution (lock-free), IBM freelists: Pre-allocate a number of nodes, link them into a dynamic stack structure, and allocate/reclaim using CAS HeadMem 1Mem 2Mem n … Used 1 Reclaim Allocate

14. Concurrent Insert vs. Delete operations Problem: - both nodes are deleted! Solution (Harris et al): Use bit 0 of pointer to mark deletion status 1 3 42 Delete Insert a) b) 1 3 42* a) b) c)

15. The ABA problem Problem: Because of concurrency (pre-emption in particular), same pointer value does not always mean same node (i.e. CAS succeeds)!!! 176 4 273 4 Step 1: Step 2:

16. The ABA problem Solution: (Valois et al) Add reference counting to each node, in order to prevent nodes that are of interest to some thread to be reclaimed until all threads have left the node 1*6* 273 4 11 ??? 1 CAS Failes! New Step 2:

17. Helping Scheme Threads need to traverse safely Need to remove marked-to-be-deleted nodes while traversing – Help! Finds previous node, finish deletion and continues traversing from previous node 1 42* 1 42* or ? ? 1 42*

18. Back-Off Strategy For pre-emptive systems, helping is necessary for efficiency and lock-freeness For really concurrent systems, overlapping CAS operations (caused by helping and others) on the same node can cause heavy contention Solution: For every failed CAS attempt, back-off (i.e. sleep) for a certain duration, which increases exponentially

19. Our Lock-Free Algorithm Based on Skip Lists Treated as layers of ordered lists Uses CAS atomic primitive Lock-Free memory management IBM Freelists Reference counting Helping scheme Back-Off strategy All together proved to be linearizable

20. Experiments 1-30 threads on platforms with different levels of real concurrency 10000 Insert vs. DeleteMin operations by each thread. 100 vs. 1000 initial inserts Compare with other implementations: Lotan and Shavit, 2000 Hunt et al An Efficient Algorithm for Concurrent Priority Queue Heaps, 1996

21. Full Concurrency

22. Medium Pre-emption

23. High Pre-emption

24. Conclusions Our work includes a Real-Time extension of the algorithm, using time-stamps and a time-stamp recycling scheme Our lock-free algorithm is suitable for both pre-emptive as well as systems with full concurrency Will be available as part of NOBLE software library, http://www.noble-library.org See Technical Report for full details, http://www.cs.chalmers.se/~phs

25. Questions? Contact Information: Address: Håkan Sundell vs. Philippas Tsigas Computing Science Chalmers University of Technology Email: @ cs.chalmers.se Web: http://www.cs.chalmers.se/~phs/warp

26. Semaphores

27. Back-off spinlocks

28. Jones Skew-Heap

29. The algorithm in more detail Insert: 1. Create node with random height 2. Search position (Remember drops) 3. Insert or update on level 1 4. Insert on level 2 to top (unless already deleted) 5. If deleted then HelpDelete(1) All of this while keeping track of references, help deleted nodes etc.

30. The algorithm in more detail DeleteMin 1. Mark first node at level 1 as deleted, otherwise HelpDelete(1) and retry 2. Mark next pointers on level 1 to top 3. Delete on level top to 1 while detecting helping, indicate success 4. Free node All of this while keeping track of references, help deleted nodes etc.

31. The algorithm in more detail HelpDelete(level) 1. Mark next pointer at level to top 2. Find previous node (info in node) 3. Delete on level unless already helped, indicate success 4. Return previous node All of this while keeping track of references, help deleted nodes etc.

32. Correctness Linearizability (Herlihy 1991) In order for an implementation to be linearizable, for every concurrent execution, there should exist an equal sequential execution that respects the partial order of the operations in the concurrent execution

33. Correctness Define precise sequential semantics Define abstract state and its interpretation Show that state is atomically updated Define linearizability points Show that operations take effect atomically at these points with respect to sequential semantics Creates a total order using the linearizability points that respects the partial order The algorithm is linearizable

34. Correctness Lock-freeness At least one operation should always make progress There are no cyclic loop depencies, and all potentially unbounded loops are gate-keeped by CAS operations The CAS operation guarantees that at least one CAS will always succeed The algorithm is lock-free

35. Real-Time extension DeleteMin operations should ignore nodes that are inserted after the DeleteMin operation started Nodes are inserted together with a timestamp Because timestamps are only used for relative comparisons, no need for a real-time clock Generate time-stamps by increasing function

36. Real-Time extension Timestamps are potentially unbounded and will overflow Recycle wrapped-over timestamp values by having TagFieldSize=MaxTag*2 Timestamps at nodes can stay forever (MaxTag => unlimited) Every operation traverses one step through the Skiplist and updates too old timestamps