Algorithm 4: RemoveComplexBulges

1: procedure RemoveComplexBulges

2: globalG

3: for alldo             ▹ s ranges over vertices in the condensed graph

4:  B ← {s}

5:  whileB ⊂ D(s) do

6:   Let v be the closest vertex to s that is in D(s) but not in B

7:   B = Closure(s, B ∪ {v})

8:   if height of B is larger than 250 orB contains more than 500 vertices then

9:    break

10:   end if

11:   ifG[B] is not a tree then                           ▹ Condition D1

12:    (S, g) ← ConstructSkeleton(B)

13:    ifS is a tree then             ▹ Necessary condition for B to have a proper skeleton

14:     j ← ConstructProperSkeleton(s, G[B], S, g)

15:     if the ConstructProperSkeleton procedure succeeded then          ▹ Condition D2

16:      Replace G[B] with a tree j(S)             ▹ Project bulge onto a proper skeleton

17:      break

18:     end if

19:    end if

20:   end if

21:  end while

22: end for

23: end procedure