A tight analysis of the Katriel-Bodlaender algorithm for online topological ordering

Katriel and Bodlaender [7] modify the algorithm proposed by Alpern et al. [2] for maintaining the topological order of the n nodes of a directed acyclic graph while inserting m edges and prove that their algorithm runs in O(min{m3/2 log n,m + n log n}) time and has an Ω(m) lower bound. In this paper, we give a tight analysis of their algorithm by showing that it runs in time Θ(m + mn log n). General Terms: Algorithms Additional