Analysis and Evaluation of Non-Blocking Interpolation Search Trees

TL;DR

This paper presents a comprehensive analysis and evaluation of a novel non-blocking concurrent interpolation search tree (C-IST), demonstrating its correctness, linearizability, and efficient wait-free and lock-free operations under various key distributions.

Contribution

It introduces the first non-blocking concurrent interpolation search tree and provides detailed correctness proofs, complexity analysis, and experimental performance evaluation.

Findings

Operations are correct and linearizable.

Lookup and non-destructive operations are wait-free.

Insert and delete are lock-free.

Abstract

We start by summarizing the recently proposed implementation of the first non-blocking concurrent interpolation search tree (C-IST) data structure. We then analyze the individual operations of the C-IST, and show that they are correct and linearizable. We furthermore show that lookup (and several other non-destructive operations) are wait-free, and that the insert and delete operations are lock-free. We continue by showing that the C-IST has the following properties. For arbitrary key distributions, this data structure ensures worst-case $O(\log n + p)$ amortized time for search, insertion and deletion traversals. When the input key distributions are smooth, lookups run in expected $O(\log \log n + p)$ time, and insertion and deletion run in expected amortized $O(\log \log n + p)$ time, where $p$ is a bound on the number of threads. Finally, we present an extended experimental evaluation of the non-blocking IST performance.