In this paper, we address the problem of finding good quality elimination orders for triangulating dynamic Bayesian networks. In Bilmes and Bartels (2003), the authors proposed a model and an algorithm to compute such orders, but in exponential time. We show that this can be done in polynomial time by casting the problem to the problem of finding a minimum s–t cut in a graph. In this approach, we propose a formal definition of an interface (a set of nodes which makes the past independent from the future), we link the notion of an interface with the notion of a graph cut-set. We also propose an algorithm which computes the minimum interface of a dBN in polynomial time. Given this interface, we show how to get an elimination order which guarantees, theoretically and experimentally, the triangulation quality.