Algorithm 2: Extended Nemhauser’s Algorithm for ${\mathcal{P}}_2$.

Input: $\mathcal{V},f,\mathcal{R},k$    Output: $\mathcal{S}$ 1 $\mathcal{S}=\{\varnothing \}$; 2 $\mathcal{S}\leftarrow$ Apply Algorithm 1 on ${\mathcal{P}}_1(f,\mathcal{V}\left\{\mathcal{R}\right\},k-|\mathcal{R}\left|\right)$; 3 $\mathcal{S}=\mathcal{S}\cup \mathcal{R}$;