Algorithm 1 Tree Alignment Using Needleman-Wunsch Algorithm

Require: a set of trees ${\tau }_1,{\tau }_2,\dots ,{\tau }_k$ Ensure: $i=1$ Ensure: $x_{seq}\leftarrow$ Perform pre-order tree traversal on ${\tau }_i$  while not end of k do   for $j=1\mathrm{to}k$ do    if $i\ne j$ then     $y_{seq}\leftarrow$ Perform pre-order tree traversal on ${\tau }_j$     $Scor{e}_{i,j}\leftarrow$ Using Equation (1), calculate similarity between $x_{seq}$ and $y_{seq}$    end if    $i=i+1$   end for  end while  ${\tau }_{max}\leftarrow$ Select tree with max of average similarity score of $Score$ matrix