Dynamic Spanning Trees for Connectivity Queries on Fully-dynamic Undirected Graphs (Extended version)

TL;DR

This paper introduces the D-tree, a novel data structure that efficiently handles connectivity queries in large fully dynamic graphs, outperforming existing worst-case guarantee data structures in practical scenarios.

Contribution

The paper presents the first scalable dynamic tree data structure for fully dynamic graphs, enabling faster average-case connectivity queries on large datasets.

Findings

D-tree scales to millions of vertices and edges.

Answers connectivity queries faster on average than existing structures.

First data structure to handle large fully dynamic graphs efficiently.

Abstract

Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data structure, the dynamic tree (D-tree), together with algorithms to construct and maintain it. The D-tree is the first data structure that scales to fully dynamic graphs with millions of vertices and edges and, on average, answers connectivity queries much faster than data structures with worst case guarantees.