(Steiner Tree Problem Heuristic) We are given a connected graph G with a nonnegative weight aij for each arc (i, j) ∈ A. We assume that if an arc (i, j) is present, the reverse arc (j, i) is also present, and aij = aji. Consider the problem of finding a tree in G that spans a given subset of nodes S and has minimum weight over all such trees. (a) Let W∗ be the weight of this tree. Consider the graph I(G), which has node set S and is complete (has an arc connecting every pair of its nodes). Let the weight for each arc (i, j) of I(G) be equal to the shortest distance in the graph G from the node i ∈ S to the node j ∈ S. Let T be a minimum weight spanning tree of I(G). Show that the weight of T is no greater than 2W