Shortest-Path for Weighted Directed Bipartite Graphs I did a research project in which I seek to move a car through zones from origin to destination. This allows for the formulation of a bipartite graph because only adjacent zones can be connected. Each edge has a non-negative weight of time. I look to find the shortest path between source and sink, given the weights and directions of the edges. The structure of the graph is quite simple, all adjacent zones are connected. The bipartite graph looks this this. 

My question is what is the best shortest-path algorithm for such a graph?
Merge every zone into one vertex. You now have a linear path, with one or multiple edges between each vertex. Since this graph does not branch, you can simply choose the cheapest edge between every vertex directly.

A small illustration I made: