Table 2 The algorithm to build range tree with fractional cascading. Input P is the original interval set. Return the root node v of the resulting range tree.

1.

Sort P by y-value, return an array of intervals P_y.

2.

if P contains only one interval i then

3.

    Creating a leaf node v_leaf storing this interval. i.e., v_leaf. interval = i

4.

else

5.

    Split P into P_left and P_right, the subsets ≤ and > the median x-value x_mid of P.

6.

    Sort P_left and P_right by y-value.

7.

    Create an FC-index I_left from P_y to P_left.

8.

    Create an FC-index I_right from P_y to P_right

9.

    v_left ← BuildRTFC(P_left)

10.

    v_right ← BuildRTFC(P_right)

11.

    Create a node v storing x_mid, I_left and I_right. v.x = x_mid; v. data = P_y;         v. lfc = I_left; v. rfc = I_right; v. lchild = v_left; v. rchild = v_right

12.

end if

13.

return v