Parallel Batched Interpolation Search Tree

TL;DR

This paper introduces a parallelized version of the Interpolation Search Tree that efficiently handles large batches of operations with logarithmic and poly-logarithmic time complexities, improving performance for ordered set operations.

Contribution

It presents the first parallel implementation of the Interpolation Search Tree optimized for batch operations under smooth data distributions.

Findings

Performs a batch of m operations in O(m log log n) work.

Achieves poly-logarithmic span for batch processing.

Enhances parallel efficiency for ordered set operations.

Abstract

Ordered set (and map) is one of the most used data type. In addition to standard set operations, like insert, delete and contains, it can provide set-set operations such as union, intersection, and difference. Each of these set-set operations is equivalent to batched operations: the data structure should process a set of operations insert, delete, and contains. It is obvious that we want these "large" operations to be parallelized. Typically, these sets are implemented with the trees of logarithmic height, such as 2-3 tree, Treap, AVL tree, Red-Black tree, etc. Until now, little attention was devoted to data structures that work better but under several restrictions on the data. In this work, we parallelize Interpolation Search Tree which serves each request from a smooth distribution in doubly-logarithmic time. Our data structure of size $n$ performs a batch of $m$ operations in $O(m \log\log n)$ work and poly-log span.