Parallel-batched Interpolation Search Tree

TL;DR

This paper introduces a parallel-batched version of the Interpolation Search Tree, enabling efficient execution of large batch operations with improved asymptotic performance for sorted set operations.

Contribution

It presents a novel parallelization of the Interpolation Search Tree, achieving asymptotically better performance for batch operations on sorted sets under certain data distribution assumptions.

Findings

Performs batch operations in O(m log log n) work

Achieves poly-logarithmic span for parallel execution

Improves efficiency over traditional tree-based data structures

Abstract

A sorted set (or map) is one of the most used data types in computer science. In addition to standard set operations, like Insert, Remove, and Contains, it can provide set-set operations such as Union,Intersection, and Difference. Each of these set-set operations is equivalent to some batched operation: the data structure should be able to execute Insert, Remove, and Contains on a batch of keys. It is obvious that we want these "large" operations to be parallelized. These sets are usually implemented with the trees of logarithmic height, such as 2-3 trees, treaps, AVL trees, red-black trees, etc. Until now, little attention was devoted to data structures that work asymptotically better under several restrictions on the stored data. In this work, we parallelize Interpolation Search Tree which is expected to serve requests 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.