Algorithm 1 Program dependency graph serialization algorithm PDG2Seq

Input: $G=\left(V,E\right)$, $V=\left\{v_1,v_2,\dots ,v_n\right\}$, $E=\left\{e_1,e_2,\dots ,e_m\right\}$  Output: Minimum graph serialization encoding $seq=\left\{s_1,s_2,\dots ,s_w\right\}$

1: initialization $seq$= (), i = 0; currentNode = v0; 2: for v in V do 3:   v.visted = −1; 4: end for 5: DFSSearch (G, currentNode, $seq$); 6: for e in E do 7:  Find the insertion position in seq according to the rule ${\prec }_T$,Insert the backtracking edge e into seq; 8: end for 9: return seq 10: Subprocedure 1 DFSSearch (G, currentNode, seq) 11:   currenINode.visited = i; 12:   for nei in currentNode.neighbors do 13:    array = () 14:    for e in E do: 15:      if e.begin == currentNode then 16:        array.add (e) 17:       end if 18:    end for 19:    e = min (Sort (array)); 20:    if q.visited == −1 then 21:      i + = 1; 22:      E.remove (e); 23:      seq.add (e); 24:      DFSearch (G,q, seq); 25:    end if 26:   end for