Optimal Dynamic Multicommodity Flows in Networks

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 ( n 2.75 ) 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 3 2 + n 2 log n } ) Katriel and Bodlaender.