加权有向图的最大成本和路径算法

Question

What algorithms are there, for weighted directed graphs, to find the maximum cost and path for going from a vertex A to a vertex K ?

I was thinking of modfied Dijkstra, but while watching and learning this algorithm, I found out it can't be used with negative weights and can't be used to find the maximum cost.

Answer 1

You could use a modified version of the A* (A-star) algorithm. I say modified but it wouldn't actually be modified. You just need an appropriate heuristic. It is a path finding algorithm, you would just need to set your heuristic to chooses the costliest path.

A* works by starting at some vertex V, and adding all of that vertex's adjacent neighbors to an open list. Then it moves, in your case, to the node with the highest cost. The previously visited node is moved to a closed list. Then all the adjacent nodes to the current node are added to the open list. And so on and so forth.

It will find your K, and if your heuristic is to always choose the costliest path, you will have the maximum cost route.

Here is A* being applied to Infinite Mario .

Answer 2

I suggest the following: choose any algorithm for minimum cost(distance) and also works with negative edges (thus Dijkstra can not be used for this). Then run this algorithm using the negation of the cost for each edge. You can use Bellman–Ford algorithm for instance.