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B Tree Formulas

Posted on 2011-05-08
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Last Modified: 2012-05-11
The Problem
g. Suppose that the file is not ordered by the key field Ssn and we want to construct a B+-tree access structure (index on SSn. Calculate (i) the orders p and p_leaf of the B+-tree; (ii) the number of leaf-level blocks needed if if blocks are approximately 69 percent full (rounded up for convenience); (iii) the number of levels needed if internal nodes are also 69 percent full (rounded up for convenience); (iv) the total number of blocks required by the B+-tree; and (v) the number of block accesses needed to search for and retrieve a record from the file - given its Ssn value - using the B+-tree.

h. Repeat part g, but for a B-tree rather than for a B+-tree. Compare your results for the B-tree and for the B+tree.

Formula for order p of a B+ tree:

(p * P) + ((p - 1) * V) < B

Formula for p_leaf of a B+ tree:

(p_leaf * (Pr * V)) + P < B

I'm thinking about part h. Here, I need a formula of some kind for a B tree. Can you help me in some way?
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Question by:JCW2
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Expert Comment

by:slightwv (䄆 Netminder)
ID: 35719676
Unfortunately we are not allowed to provide answers to homework/exam questions.

Please review:
http://www.experts-exchange.com/help.jsp#hs=23&hi=21
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Accepted Solution

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BigRat earned 2000 total points
ID: 35719815
There are masses of analyses for B-Trees (as k-ary trees) on the web, here's one :-

http://www.cs.utsa.edu/~carola/teaching/cs5633/spring06/slides/Lecture-Btrees.pdf

Incidentally how old is this question? A block size of 512 bytes comes out of the eighties. Today you don't get clusters less than 32K.
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LVL 58
ID: 35719921
<<Incidentally how old is this question? A block size of 512 bytes comes out of the eighties. Today you don't get clusters less than 32K. >>

  Disk cluster yes, but many DBMS's operate with blocking other then disk cluster size.  OpenVMS still operates with blocking of 512 bytes to this day for everything.

JimD.
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Assisted Solution

by:BigRat
BigRat earned 2000 total points
ID: 35719975
Wow!

Incidentally the data is only 3.4 Megabytes. It and all possible keys would fit into memory these days.
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Author Closing Comment

by:JCW2
ID: 35725385
Thank you for your help.
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