Improved Fully Dynamic Reachability Algorithm for Directed Graph

TL;DR

This paper introduces a deterministic fully dynamic reachability algorithm for directed graphs that efficiently updates reachability information with improved performance over previous methods, supporting quick queries after updates.

Contribution

It combines existing algorithms with witness counting to enhance efficiency, especially for edge deletions, achieving better update times in dynamic graph scenarios.

Findings

Update time improved by a factor of O(n^2 / (m + n log n))

Queries answered in O(1) time after each update

Effective handling of edge deletions in dynamic graphs

Abstract

We propose a fully dynamic algorithm for maintaining reachability information in directed graphs. The proposed deterministic dynamic algorithm has an update time of $O((ins*n^{2}) + (del * (m+n*log(n))))$ where $m$ is the current number of edges, $n$ is the number of vertices in the graph, $ins$ is the number of edge insertions and $del$ is the number of edge deletions. Each query can be answered in O(1) time after each update. The proposed algorithm combines existing fully dynamic reachability algorithm with well known witness counting technique to improve efficiency of maintaining reachability information when edges are deleted. The proposed algorithm improves by a factor of $O(\frac{n^2}{m+n*log(n)})$ for edge deletion over the best existing fully dynamic algorithm for maintaining reachability information.