For a given multigraph find the size of smallest set of vertices such that every vertex in multigraph is in set, or is connected with at least one vertex contained in set.

Can it be solved better than in O(2^n) ?

Answer:

You might be able to optimize it slightly, but generally speaking - you cannot get sub-exponential time, this is the Vertex Cover Problem, which is known as NP-Hard, which means there is no known polynomial solution and the general belief is there is none.

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