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 -Add, Remove and 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 Remove operations during traversal, and, adapt to interval contention. However, for write-heavy situations we let an operation help pending Remove, even though it is not obstructed, and so adapt to tighter 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.

The amortized complexity of non-blocking binary search trees

“…Fomitchev and Ruppert [8] refined this idea to produce a singly-linked list with good amortized complexity. In these proceedings, Chatterjee, Nguyen and Tsigas use a similar approach in their implementation of a threaded node-oriented BST [6], which they claim is linearizable and achieves the same complexity as our BST. In their implementation, each node stores additional pointers that can be followed to return to an active part of the tree from a deleted node.…”

Concurrent Linearizable Nearest Neighbour Search in LockFree-kD-tree

“…This arrangement allows each node, as in an internal BST representation [10], to be used for storing data.…”

“…However, removing a node from an internal BST is costly, more so in a concurrent setting [8,10]. With this in mind, we opt for an external BST representation [7,9] to design the LFkD-tree.…”

Contention Adapting Search Trees

“…Since Fraser's algorithm, several lock-free binary search trees have been proposed (e.g. [7], [10], [15], [20], [26], [27]). The relaxed balancing external lock-free tree by Brown et al…”

“…Current scalable data structures for concurrent ordered sets and maps either use fine-grained locking [2], [6], [12], [14] or lock-free techniques [7], [10], [15], [16], [20], [26], [27] to enable parallel operations in the tree. For fine-grained synchronization, they all pay a price in sequential efficiency and/or memory usage.…”