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{m 3/2 log n, m 3/2 + n 2 log n}) time and has an Ω(m 3/2 ) lower bound. In this paper, we give a tight analysis of their algorithm by showing that it runs in time Θ(m 3/2 + mn 1/2 log n) 1 .
In REF , we proved that the Katriel-Bodlaender algorithm takes Θ(m 3/2 + mn 1/2 log n) time for inserting m edges.
A Tight Analysis of the Katriel-Bodlaender Algorithm for Online Topological Ordering
Theor. Comput. Sci.
Theor. Comput. Sci.
Mathematics Computer Science