jis
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Time to go and re-learn what NP Complete means I am afraidApologize in advance for being a technonerd.
And I might be wrong.
BUT -- I think - the problem of finding all possible connections on published schedules is "NP-complete" or possibly less if the number of connections and departure times is small.
For big systems with small time constraints, like days almost certain that there are so many ways to get from A to B in the next week that no computer can possibly figure them all. Proven computational fact.