Given a Weighted Undirected Graph G = (V,E), and a subset S of V, How we can find a minimum cost cycle that contains every vertex of set S. You can visit every vertex & edge any number of times.

constraints:

#1: weight of edges are positive

#2: Size of set V is less than 100

#3: Size of set E is less than 500

#4: Each vertex of set V is reachable from every other vertex i.e. Graph G is connected.

Any insights , resources or help to solve the problems including cycles are welcomed.

Thank you very much for your help & time.