Fast Dynamic Arrays

TL;DR

This paper introduces an optimized implementation of tiered vectors that significantly improves access, insertion, and deletion times for large sequences, outperforming standard library structures in speed and space efficiency.

Contribution

The paper presents a highly optimized C++ implementation of tiered vectors with superior performance and lower space usage compared to standard library data structures.

Findings

40x faster access than multiset

10,000x faster insertion/deletion than vector

Uses less space than multiset

Abstract

We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of $n$ elements supporting access in time $O(1)$ and insertion and deletion in time $O(n^\epsilon)$ for $\epsilon > 0$ while using $o(n)$ extra space. We consider several different implementation optimizations in C++ and compare their performance to that of vector and multiset from the standard library on sequences with up to $10^8$ elements. Our fastest implementation uses much less space than multiset while providing speedups of $40\times$ for access operations compared to multiset and speedups of $10.000\times$ compared to vector for insertion and deletion operations while being competitive with both data structures for all other operations.