The CB tree: a practical concurrent self-adjusting search tree

Abstract

We present the CB tree, a counting-based self-adjusting binary search tree in which, as in splay trees, more-frequently accessed items move closer to the root. In a sequential execution, after $m$ operations of which $c(v)$ access item $v$, an access of $v$ traverses a path of length $\mathcal {O}\left( 1 + \log \frac{m}{c(v)}\right)$ while doing few if any rotations. Unlike the original splay tree, in which each access moves the accessed item all the way to the root via a sequence of rotations, accesses in a CB tree do very few rotations, specifically $\mathcal {O}\left( n + n\log \frac{m}{n}\right)$, during a sequence of $m$ operations of which $n$ are insertions. This is $o(1)$ (subconstant) amortized per operation if $m \gg n$. We adapt the CB tree into a scalable concurrent self-adjusting BST. We show experimentally that the concurrent CB tree scales well because it, too, performs few rotations, and therefore self-adjusts without having rotations create a bottleneck. Our evaluation shows that the concurrent CB tree performs better than existing concurrent search trees on non-uniform access sequences derived from real workloads.