Table 4 Fast density modifications

2:    Set currentNode ← head of tree T

3:    while currentNode is not a leaf do

4:       if currentCoord > currentNode.vpartition then

5:          if currentCoord > currentNode.hpartition then

6:             Set currentNode ← currentNode.topRight

7:          else Set currentNode ← currentNode.bottomRight

8:          end if

9:       else

10:          if currentCoord > currentNode.hpartition then

11:             Set currentNode ← currentNode.topLeft

12:          else Set currentNode ← currentNode.bottomLeft

13:          end if

14:       end if

15:    end while

16:    for all node in Set currentNode do

17:       Add density ← $\frac{Log(NodeBC[node]+1)}{Distance{(v,node)}^2}$

18:       if v and node overlap then

19:          Return ∞

20:       end if

21:    end for

22:    Return density

23: end procedure

24: procedure FAST PLACE NODE(v,v^')

25:    Set v.coordinate ← Coordinate generated by a Gaussian centered at v'.coordinate with variance c₁N odeBC [v]²

26:    Anneal(v,threshold)

27:    Push v → S

28: InsertNode(v) ▹ Node insertion to tree added

29:    Get set of nodes ← values in H with key v ▹ Get orphans which can now be placed

30:    for all node in nodes do

31:       PlaceNode(node,v)

32:    end for

33: end procedure

34: procedure INSERT NODE(v)

35:    Set currentN ode ← head of tree T

36:    while currentN ode is not a leaf do

37:       if currentCoord > currentN ode.vpartition then

38:          if currentCoord > currentN ode.hpartition then

39:             Set currentN ode ← currentN ode.topRight

40:          else Set currentN ode ← currentN ode.bottomRight

41:          end if

42:       else

43:          if currentCoord > currentN ode.hpartition then

44:             Set currentN ode ← currentN ode.topLef t

45:          else Set currentN ode ← currentN ode.bottomLef t

46:          end if

47:       end if

48:    end while

49:    currentN ode.add(v)

50:    while currentN ode.size > maxT reeSize do²²

51:       Set currentN ode.topRight ← currentN ode.partitionT opRight

52:       Set currentN ode.topLeft ← currentN ode.partitionT opLef t

53:       Set currentN ode.bottomRight ← currentN ode.partitionBottomRight

54:       Set currentN ode.bottomLeft ← currentN ode.partitionBottomLef t

55:    end while

56: end procedure