Algorithm 1 Pruned Dynamic Programming Algorithm

procedure$GenerateLayer(orderGraph)$

1. for each $parentGraph$ $pg$ do

2. $generateParentLayer(pg)$

3. end for

4. for each node $O\in prev$ do

5. for each $v\in V-O$ do

6. $pg\leftarrow parentGraphs[v].readNode()$

7. $score\leftarrow pg.score+O.score$

8. if $score<curr[O\cup v].score$ then

9. $curr[O\cup v]\leftarrow \{O.pars\cup pg.pars,score\}$

10. end if

11. if $v=Y_1$ then $write(curr[O\cup v])$

12. end for $[each$ $v]$

13. end for $[each$ $node$ $O]$

14. $prev\leftarrow curr$

15. $curr\leftarrow newHashTable$

end procedure

procedure$GenerateParentLayer(pg)$

16. for each node $P\in MB$ do

17. for each $v\in V-P$ and $v\ne pg.v$ do

18. if $curr[P\cup v]$ is null then

19. $curr[P\cup v]\leftarrow \{P\cup v,score(P\cup v)\}$

20. end if

21. if $P.score<curr[P\cup v].score$ then

22. $curr[P\cup v]\leftarrow P$

23. end if

24. if $v=p_1$ then $write(curr[P\cup v])$

25. end for $[each$ $v]$

26. end for $[each$ $node$ $P]$

27. $prev\leftarrow currentLayer$

28. $curr\leftarrow newHashTable$

end procedure

proceduremain

29. for $l=1\to n$ do

30. $GenerateLayer(orderGraph)$

31. end for

end procedure