1. Lock-Free Binary Search Tree Presented by Joanna Helga

2. Leaf Oriented Binary Search Tree Implements Dictionary ADT Operations: Find, Insert, Delete Real keys are stored in leaf Internal nodes stores dummy keys and exactly has 2 children Leaves stores only a key B A D C G EH

3. Node Implementation Node LeafInternal left : Node right : Node key : int 2

4. Dictionary Implementation Dictionary root : Internal Dictionary() Find() : Leaf Insert(int) : boolean Delete(int) : boolean ∞2∞2 ∞1∞1 ∞2∞2 root is always Internal Node

5. Insert Insert(E) search for location create Leaf(E) create Internal(max(E,D)) point its left and right child to D and E Flag B change B’s pointer to the new Internal node Unflag B B D α E E B

6. Flagging a node  Atomically set the node’s status to Flag and set it’s helper pointer to a Helper Node  4 Kinds of Node’s status:  Clean  IFlag  DFlag  Mark A Helper Node A

7. Implementation  Using AtomicStampedReference HelperNodeint 0=Clean1=IFlag2=DFlag3=Mark

8. HelperNode Implementation Flag p : Node l : Node IFlag newinternal: Node DFlag gp : Node pupdate : AtomicStampedReference Internal left : Node right : Node update : AtomicStampedReference

9. Delete Delete(C) Search C’s location Flag B (grandparent) Mark D (parent) Change B’s child pointer to C’s sibling Unflag B B D α C β B D

10. CAS-Child  Many processes can try to help one operation  Use CAS to change child pointer to ensure only one process successful B D α E E B α β InsertDelete

11. Blocking BST  Implemented using synchronization Node LeafInternal left : Node right : Node key : int 2 Dictionary root : Internal Dictionary() Find() : Leaf Insert(int) : boolean Delete(int) : boolean Not using Helper Node

12. Search public SearchRet Search(int key){ synchronized(this){ this.activereaders++; } // traverse the tree synchronized(this){ this.activereaders--; if(this.activereaders == 0) this.notify(); } // return }

13. Insert public boolean Insert(int key){ // create new leaf and new sibling // create parent for them synchronized(this){ while(this.activereaders != 0){…} // modify BST this.notify(); }

14. Delete public boolean Delete(int key){ // find l's sibling synchronized(this){ while(this.activereaders != 0){…} // modify BST this.notify(); }

15. Performance Comparison: Add Only  Blocking Algorithm

16. Performance Comparison: Add Only  Non-Blocking Algorithm

17. Performance Comparison: Add Only  Blocking V.S. Non-Blocking