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

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.

Better results have been proposed in the following paper: Haeupler, Kavitha, Mathew, Sen, Tarjan: Faster Algorithms for Incremental Topological Ordering. ICALP (1) 2008: 421-433