Efficient Lock-free Binary Search Trees

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 - {\sc Add}, {\sc Remove} and {\sc Contains} - is $O(H(n) + c)$, where, $H(n)$ is the height of 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 pending concurrent {\sc Remove} operations during traversal, and, adapt to interval contention. However, for write-heavy situations we let an operation help pending {\sc Remove}, even though it is not obstructed, and so adapt to tighter point contention. It uses single-word compare-and-swap (\texttt{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.