Algorithm 2. Pseudo code of node-choosing sub-algorithm.

Algorithm 2 Description: node-choosing sub-algorithm (pick out one node at Level 1, into which TNode will be inserted)

Input: TNode (leaf node to insert into R-tree), Root (the root of R-tree)

Output: a level-one node (considered as the father of TNode)

1. NodeSet.Clear()            : temporal node set is cleared off

2. MinLevelID → Root.LevelID + 1     : let MinLevelID be tree depth initially

3. Father → Root           : let Father be Root

4. SeqArray[Father.LevelID] → 0;      : let the Father.LevelIDth item in SeqArray be 0

5. While Father != NULL Do

6. Node → Father.IthChild (SeqArray[Father.LevelID])     : let the ith child of Father be the current node

7. If Node.Contain(TNode) = True Then     : if Node contains TNode

8. If Node.LevelID = MinLevelID Then     : if level number of Node is equal to MinLevelID

9. NodeSet.Add(Node)     : add Node in NodeSet

10. Else If Node.LevelID < MinLevelID Then     : if level number of Node is less than MinLevelID

11. NodeSet.Clear()     : clear NodeSet

12. NodeSet.Add(Node)     : add Node in NodeSet

13. MinLevelID → Node.LevelID     : let MinLevelID be level number of Node

14. End If

15. If Node.LevelID > 1 Then     : if level number of Node is greater than 1, enter the lower level

16. Father → Node     : let Father be Node

17. SeqArray[Father.LevelID] → 0     : let the corresponding item in SeqArray 0

18. Continue Loop     : restart new loop

19. End If

20. End If

21. If Node.LevelID = 1 Or Node.Contain(TNode) = False Then     : if Node is at level 1 or Node doesn't contain Leaf

22. SeqArray[Father.LevelID] → SeqArray[Father.LevelID] + 1     : move to next child node

23. While SeqArray[Father.LevelID] = Father.NumChildren Do     : if finish traversing all child nodes

24. Father → Father.ParentNode     : backspace to upper level

25. If Father = NULL Then     : if finish traversing all child nodes of Root

26. Break Loop     : exit loop

27. End If

28. SeqArray[Father.LevelID] → SeqArray[Father.LevelID] + 1     : start traversing the right sibling

29. End While

30. End If

31. End While

32. If NodeSet.IsEmpty() = True Then     : if NodeSet is null, there is no node to contain TNode

33. NewRoot → Root     : let NewRoot be Root

34. Else If MinLevelID = 1 Then     : if there exist the required nodes at level 1

35. NewRoot → LargestNode(NodeSet)     : let NewRoot be the largest node in NodeSet

36. Else

37. Set is the collection of child nodes of all nodes in NodeSet. In Set, choose a node which will change the least after containing TNode. Let NewRoot be the node

38. End If

39. In the sub-tree whose root is NewRoot, search for a node in level 1 by classical node choosing algorithm.

40. Output the node. Exit