Assume that you have a tree clustered index on a table of 100,000 tuples where
• A page can hold 20 data tuples
• An index page can have up to 100 pointers
What is the minimum possible number of levels such an index can have? Draw a sketch of such an index and of the table that it indexes.
Solution:
The table has 100000/20 = 5000 pages. Since the index is clustered, the index can be sparse with 1 pointer per page, so it needs 5000 pointers. The minimum number of levels will result if the nodes of the tree are maximally packed. Thus, the minimum depth is ceiling(log1005000) = 2.
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