Computing Directed Pathwidth in $$O(1.89^{n})$$O(1.89n) Time

We give an algorithm for computing the directed pathwidth of a digraph with n vertices in $$O(1.89^{n})$$O(1.89n) time. This is the first algorithm with running time better than the straightforward $$O^{*}(2^n)$$O?(2n). As a special case, it computes the pathwidth of an undirected graph in the same amount of time, improving on the algorithm due to Suchan and Villanger which runs in $$O(1.9657^n)$$O(1.9657n) time.