An O(n) algorithm for online topological ordering?

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n2.75) time, independent of the number of edges m inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m 3 2 log n,m 32 + n log n}) by Katriel and Bodlaender. We also provide an empirical comparison of our algorithm with other algorithms for online topological sorting.