An $\tilde{O}(n^{2.5})$-Time Algorithm for Online Topological Ordering

TL;DR

This paper introduces an efficient algorithm with approximately O(n^{2.5}) time complexity for dynamically maintaining the topological order of a directed acyclic graph as edges are added, improving performance for large graphs.

Contribution

It presents a novel algorithm that significantly reduces the time complexity for online topological ordering compared to previous methods.

Findings

Achieves O(n^{2.5}) time complexity for online topological ordering

Efficiently updates topological order with each edge insertion

Applicable to large-scale directed acyclic graphs

Abstract

We present an $\tilde{O}(n^{2.5})$-time algorithm for maintaining the topological order of a directed acyclic graph with $n$ vertices while inserting $m$ edges.