Fully Dynamic Breadth First Search and Spanning Trees in Directed Graphs

TL;DR

This paper introduces a framework for maintaining BFS trees and related structures in directed graphs under fully dynamic edge updates, addressing a less-explored area in dynamic graph algorithms.

Contribution

It provides a novel framework and data structures for fully dynamic BFS, including spanning trees, levels, and numbering, in directed graphs.

Findings

Supports both insertions and deletions in directed graphs.

Maintains BFS trees, shortest paths, and reachability dynamically.

Addresses a gap in fully dynamic graph algorithms.

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.