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I will try to make clear analogy:

There is a city with N destinations. It is represented by weighted and directed graph where weights are distances as minutes.

There are 2 people which don't want to be in same destination at same time. They are located in different destinations. They are going to go to another destinations using shortest paths without being in same destination at all. They will stay M minutes in each visited destination.

How to find shortest path while keeping them distant?

NOTE: I have looked shortest path algorithm, traveling salesman algorithm and thier variations. But I can't figure out how to solve it effectively. Finding all paths and comparing intersections doesn't look cost efficient.

Samed Kahyaoglu
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  • Need some clarification around "stay M minutes in each visited destination". This implies that the graph not only has edge weights, but also vertex weights. Let's say John wants to go from A to Z and the shortest path is A -> B -> D -> F -> Z. Let's say Dave wants to go from C to X and the shortest path is C -> E -> F -> X. They may or may not meet at F depending on the time taken to travel between each destination, as well as time spent in each destination along the way to their respective final destinations. The goal is not ensure that they do never meet. Correct? – wookie919 Dec 22 '20 at 21:49

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