Before revision:  We further show that the techniques developed in this work can also lead to simple algorithms for the All Pairs Non-Decreasing Paths Problem (APNP) on undirected graphs, matching the asymptotically optimal running time of O(n^2) provided in the recent work of Duan et al. (ICALP'19).
After revision:  We further show that the techniques developed in this work can also lead to simple algorithms for the All Pairs Non-Decreasing Paths Problem (APNP) on undirected graphs, matching the near-optimal running time of O(n^2) provided in the recent work of Duan et al. (ICALP'19).