Efficient lock-free binary search trees

Bapi Chatterjee, Nhan Nguyen Dang, Philippas Tsigas

Abstract: In this paper we present a novel algorithm for concurrent lock-free internal binary search trees (BST) and implement a Set abstract data type (ADT) based on that. We show that in the presented lock-free BST algorithm the amortized step complexity of each set operation - Add, Remove and Contains - is O(H(n) + c), where H(n) is the height of the BST with n number of nodes and c is the contention during the execution. Our algorithm adapts to contention measures according to read-write load. If the situation is read-heavy, the operations avoid helping the concurrent Remove operations during traversal, and adapt to interval contention. However, for the write-heavy situations we let an operation help a concurrent Remove, even though it is not obstructed. In that case, an operation adapts to point contention. It uses single-word compare-and-swap (CAS) operations. We show that our algorithm has improved disjoint-access-parallelism compared to similar existing algorithms. We prove that the presented algorithm is linearizable. To the best of our knowledge, this is the first algorithm for any concurrent tree data-structure in which the modify operations are performed with an additive term of contention measure.