Given: undirected weighted connected graph. s,t are vertices.
Question: Find an algorithm as efficient as possible that returns a path from s to t. In that path, the edge that has the highest weight, will has the least weight as possible. So if we have 5 paths from s,t and for every path we have the heaviest edge, so the minimum edge of these 5.
What I've tried:
- Use some algorithm to find the shortest path between s and t.
- Delete all the edges that are not part of the shortest paths we've found
- Use BFS with some modification, We run BFS depending on the number of paths from s to t. Every time we find a maximum edge and store it in an array, then we find the minimum of the array.
I'm struggling to find an algorithm that can be ran in (1), Bellman ford won't work - because it has to be directed graph. Dijkstra won't work because we don't know if it has negative circles or negative edges. And Prim is for finding MST which I'm not aware of how it can help us in finding the shortest path. Any ideas?
And other from that, If you have an algorithm in mind that can solve this question, would be much appreciated.