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[–] SelfReferenceParadox ago 

Just off the top of my head, it sounds to me like this may reduce to the Travelling Salesman Problem, making this a very difficult problem to solve for large data sets, like you wanted. If you're OK with getting a non-optimal answer, some kind of heuristic.

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[–] CaptainParanoia ago 

Not quite, TSP visits all nodes. And there is software like CONCORDE that can handle very large instances.