Simple and Efficient Fully-Functional Succinct Trees

TL;DR

This paper introduces a simplified, practical variant of a succinct tree data structure that achieves faster worst-case operation times and outperforms existing implementations in experiments.

Contribution

A new, simpler variant of the fully-functional succinct tree with worst-case $O( ext{log log } n)$ operation time, improving practicality and performance.

Findings

Experimental results show superior performance over existing implementations.

The new variant is easier to implement while maintaining efficient operation times.

Achieves worst-case $O( ext{log log } n)$ time complexity for tree operations.

Abstract

The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using $2n+o(n)$ bits. However, the full idea is hard to implement. Only a simplified version with $O(\log n)$ operation time has been implemented and shown to be practical and competitive. We describe a new variant of the original idea that is much simpler to implement and has worst-case time $O(\log\log n)$ for the operations. An implementation based on this version is experimentally shown to be superior to existing implementations.