Fully Dynamic Breadth First Search and Spanning Trees in Directed Graphs
Data Structures and Algorithms
2026-04-15 v1
Abstract
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering together in the fully dynamic setting is less developed. This preprint presents a framework for fully dynamic BFS in directed graphs together with supporting data structures for maintaining the BFS tree, single-source shortest paths, and single-source reachability under both insertions and deletions.
Keywords
Cite
@article{arxiv.2604.12370,
title = {Fully Dynamic Breadth First Search and Spanning Trees in Directed Graphs},
author = {Gregory Morse and Tamás Kozsik},
journal= {arXiv preprint arXiv:2604.12370},
year = {2026}
}
Comments
12 pages, 3 figures, 2 algorithms