The Design of Approximation Algorithms $|1$st Edition

Chapter $2,$ Problem $9$E$.$ Current solution is not correct.

Here is the question: Problem

As given in Exercise $2\mathrm{.}5,$ in the Steiner tree problem we are given an undirected graph G $=($V$,$ E$)$ and a set of terminals R $$ V$.$ A Steiner tree is a tree in G in which all the terminals are connected; a nonterminal need not be spanned. Show that the local search algorithm of Section $2\mathrm{.}6$ can be adapted to find a Steiner tree whose maximum degree is at most $2$ OPT $+$log$2$ n$,$ where OPT is the maximum degree of a minimum$-$degree Steiner tree.

The answer needs to have algorithm, proof of run time as well as proof of approxmination ratio