Very good points. I wonder what this means for real-world street network graphs. In my experience, m can be considered proportional to n in road network graphs (I would estimate m ≈ 2C n, with C being between 2 and 3). This would mean that the asymptotic running time of this new algorithm on a classic road transportation network would be more like O(Cn log^2/3 n) = O(n log^2/3 n), so definitely better than classic Dijkstra (O(n log n) in this scenario). On the other hand, the frontier in road network graphs is usually not very big, and (as you also said for grid graphs) you normally never "max out" the priority queue with n nodes, not even close. I would be surprised if the ^2/3 beats the additional constant overhead of the new approach in this case.