Consider how the monotonicity constraint affects the standard shortest path algorithms (like Dijkstra's or Bellman-Ford). How would you modify these algorithms to ensure the path remains monotonic in weight?

Explore the idea of maintaining a "monotonicity frontier" during the path construction. How can you use this to prune or prioritize edges while ensuring the path remains monotonic?

Investigate the possibility of transforming the problem into a layered graph problem, where each layer represents a monotonic segment of the path. How would you model the edges between layers to ensure the shortest path remains monotonic?