Compreender os caminhos minimax / maximin (Floyd-Warshall)

Question

Eu implementei o algoritmo Floyd-Warshall para resolver o problema do caminho mais curto de todos os pares.Agora eu descobri que também posso calcular o caminho Minimax ou Maximin com fácil modificações.Mas eu não entendo o que é o resultado (o que é um caminho de minimox).Eu encontrei alguns explicações na web, mas eles estão me confundindo.

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minimax - Minimax em problemas de gráfico envolve encontrar um caminho entre dois nós que minimizam o custo máximo ao longo do caminho.

maximin - o contrário de Minimax - Aqui você tem problemas em que você precisa encontrar o caminho que maximiza o custo mínimo ao longo de um caminho.

Alguém poderia tentar dar uma outra explicação ou um exemplo?

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!