Algorithm 2SinglePath($B_r$,P,K,i,j)

1:for ($p=P$ to 2; $p--$) do 2:   Acquire the set ${\mathcal{G}}_{p,K}^{\langle i,j\rangle }$; 3:   for ($k=1$ to K; $k++$) do 4:     if ($SA\_Reuse$($B_r$,$r_{p,k}^{\langle i,j\rangle }$) = $true$) then 5:       return $Accepted$; 6:     end if 7:   end for 8: end for 9:return $Blocked$;