Succinct data structure for dynamic trees with faster queries

TL;DR

This paper improves a dynamic succinct data structure for trees by reducing query times for certain operations from logarithmic to sub-logarithmic, enhancing efficiency for dynamic tree management.

Contribution

It introduces optimized algorithms that lower the query time complexities for specific tree operations in dynamic succinct data structures.

Findings

Degree and level_ancestor queries now run in O(log n / log log n) time

Overall query performance is improved over previous structures

Maintains efficient updates with O(log n) insertion/deletion times

Abstract

Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in $O(\log n)$ time. In this paper we improve the result of Navarro and Sadakane by reducing the time complexities of some queries (e.g.\ degree and level\_ancestor) from $O(\log n)$ to $O(\log n/\log\log n)$.