Succinct Euler-Tour Trees

TL;DR

This paper presents a space-efficient data structure for Euler-tour trees that enables fast queries and updates on forests, significantly reducing memory usage while maintaining performance.

Contribution

It introduces a novel succinct representation of Euler-tour trees that supports efficient operations with minimal space overhead.

Findings

Uses 2n + o(n) bits for storage

Supports constant-time simple queries

Supports polylogarithmic amortized updates

Abstract

We show how a collection of Euler-tour trees for a forest on $n$ vertices can be stored in $2 n + o (n)$ bits such that simple queries take constant time, more complex queries take logarithmic time and updates take polylogarithmic amortized time.