The shortest way to visit all metro lines in Paris
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What if {a tourist, a train addict, Dr. Sheldon Cooper, somebody who likes to waste time} wants to visit all metro lines or carriages in a given network in a minimum number of steps? We study this problem with an application to the Parisian metro network and propose optimal solutions thanks to mathematical programming tools. Quite surprisingly, it appears that you can visit all 16 Parisian metro lines in only 26 steps (we denote by a step the act of taking the metro from one station to an adjacent one). Perhaps even more surprisingly, adding the 5 RER lines to these 16 lines does not increase the size of the best solution.
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