فهم مسارات Minimax / Maximin (Floyd-Warshall)

Question

لقد قمت بتنفيذ خوارزمية Floyd-Warshall لحل مشكلة أزواج All-pairs أقصر مسار.الآن اكتشفت أنني أستطيع أيضا حساب مسار MiniMax أو Maximin بتعديلات سهلة.لكنني لا أفهم ما تعني هذه النتيجة (ما هو مسار minimax).لقد وجدت بعض تفسيرات على الويب، لكنها مربكة لي.

minimax - ينطوي minimax في مشاكل الرسم البياني على العثور على مسار بين العقدتين التي تقلل من الحد الأقصى للتكلفة على طول المسار.

maximin - في الاتجاه الآخر من minimax - هنا لديك مشاكل حيث تحتاج إلى العثور على المسار يزيد من الحد الأدنى من التكلفة على طول المسار.

هل يمكن لأي شخص أن يحاول إعطاء تفسير آخر أو مثال؟

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!