The amortized complexity of non-blocking binary search trees

Abstract

We improve upon an existing non-blocking implementation of a binary search tree from single-word compare-and-swap instructions. We show that the worst-case amortized step complexity of performing a Find, Insert or Delete operation op on the tree is O(h(op)+c(op)) where h(op) is the height of the tree at the beginning of op and c(op) is the maximum number of operations accessing the tree at any one time during op. This is the first bound on the complexity of a non-blocking implementation of a search tree.