Entendiendo los caminos Minimax / Maximin (Floyd-Warshall)

Question

He implementado el algoritmo Floyd-Warshall para resolver el problema del camino más corto de todos los pares.Ahora descubrí que también puedo calcular la ruta Minimax o Maximin con modificaciones fáciles.Pero no entiendo lo que significa el resultado (lo que es un camino de Minimax).Encontré algo explicaciones en la web, pero me confunden.

minimax - Minimax en problemas de gráficos implica encontrar un camino entre dos nodos que minimiza el costo máximo a lo largo de la ruta.

Maximin: al revés de Minimax: aquí tiene problemas en los que necesita encontrar la ruta que maximiza el costo mínimo a lo largo de un camino.

¿Podría alguien intentar dar otra explicación o un ejemplo?

Answer 1

To understand maximin paths (often called bottleneck paths) in a graph, consider the following problem. You have a road map of a country as a graph where each node represents an intersection and each edge represents a road. Each road has a weight limit, and if you drive a truck that exceeds the limit over that road it will break. You have a truck that you want to drive from some start location to some end location, and you want to put the maximum possible amount of weight on it. Given this, what path should you drive the truck in order to send the maximum possible weight?

If you think about this problem, for any path that you take in the graph, the maximum weight you can send along that path is going to be determined by the edge on that path with the minimum capacity. As a result, you want to find the path from the start to the destination whose minimum-capacity edge is maximized. The path with this property is called the maximin path or bottleneck path, and can be found with a straightforward set of modifications to mot shortest-path algorithms.

The minimax path represents the opposite idea - the path between two points that minimizes the maximum edge capacity.

Hope this helps!