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Sarah starts doing some jogging in her neighborhood recently. She wants a short simple cycle that starts and ends at her apartment building and consists

Sarah starts doing some jogging in her neighborhood recently. She wants a short simple cycle that starts and ends at her apartment building and consists of unduplicated streets. She generalizes her problem to a graph problem: given a weighted undirected graph (, ) with positive edge weights: :   R+ and a vertex   , how to find a non-empty simple cycle (which means a cycle that contains at least one edge and no repeating vertices) containing  with minimum weight? 

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