Searching in Dynamic Tree-Like Partial Orders

TL;DR

This paper introduces the Line-Leaf Tree, a novel data structure for efficiently maintaining and searching dynamic sets within tree-like partial orders, achieving near-optimal performance relative to the order's width.

Contribution

The paper presents the first data structure for dynamic set operations in tree-like partial orders, with performance close to the theoretical optimum.

Findings

Supports insert, delete, membership, and predecessor operations

Performance within an O(log w) factor of optimal

Linear size of the data structure

Abstract

We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the operations: insert; delete; test membership; and predecessor. The performance of our data structure is within an O(log w)-factor of optimal. Here w <= n is the width of the partial-order---a natural obstacle in searching a partial order.