Fault Tolerant and Fully Dynamic DFS in Undirected Graphs: Simple Yet Efficient

TL;DR

This paper introduces a simple, efficient, and fault-tolerant algorithm for maintaining DFS trees in undirected graphs, improving on existing methods in simplicity, space, and time complexity.

Contribution

It presents a novel, simplified algorithm for fault-tolerant and fully dynamic DFS in undirected graphs with optimal space and preprocessing time.

Findings

Simpler than existing algorithms

Achieves better time complexity

Uses optimal space and preprocessing time

Abstract

We present an algorithm for a fault tolerant Depth First Search (DFS) Tree in an undirected graph. This algorithm is drastically simpler than the current state-of-the-art algorithms for this problem, uses optimal space and optimal preprocessing time, and still achieves better time complexity. This algorithm also leads to a better time complexity for maintaining a DFS tree in a fully dynamic environment.