Algorithm 2 Approximation Response

1:$\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}:y ;$

2:$\mathit{o}\mathit{u}\mathit{t}\mathit{p}\mathit{u}\mathit{t}: D;$

3:$D_{appro}=\varnothing ;$

4:$\mathit{f}\mathit{o}\mathit{r} v\in V \mathit{d}\mathit{o};$

5:  $D\leftarrow \left\{v\right\};$

6:  $\mathit{w}\mathit{h}\mathit{i}\mathit{l}\mathit{e} \left|D\right|<k \mathit{d}\mathit{o};$

7:    $v^{*}\leftarrow arg ma{x}_v{U}_d\left(D{\displaystyle \cup }\left\{v\right\},\mathit{y}\right)$;

8:    $D\leftarrow \mathit{D}{\displaystyle \cup }\left\{v^{*}\right\};$

9:$\mathit{w}\mathit{h}\mathit{i}\mathit{l}\mathit{e} \left|D\right|<B do$;

10:      $D\leftarrow D{\displaystyle \cup }\left\{v\right\} choose v from V randomly;$

11:   if$U_d\left(D,y\right)>U_d\left(x,y\right) then;$

12:     $D_{appro}=D_{appro}{\displaystyle \cup }\left\{D\right\}$;

13:    $\mathit{r}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n} D_{appro};$

14:   else;

15:   return null.