Fall 2021

1. [10 marks] Suppose you have a directed graph and a start vertex s. You want to find paths from s to every other vertex. Rather than finding shortest paths (i.e., minimizing the sum of the weights of the edges in a path) you want to minimize the maximum weight of an edge in the path. We call these “max-edge shortest paths.” [For example, you are considering buying an electric car and wondering what battery power is good enough for your needs. The vertices of the directed graph are the charging stations, and the weight of an edge is the distance between the charging stations. To travel from your starting vertex s to some vertex v, you want a route that minimizes the maximum distance between any two consecutive charging stations along the route, since that corresponds to the battery strength you need in order to get from s to v, assuming you charge the battery at the charging stations.]