Wednesday, March 28, 2018

Memory required for external sorting in DBMS

Memory required for external sorting in DBMS

Let us suppose that you have a file with 150000 pages and 45 available buffer pages. If you use external sorting to sort the above said file, answer the following questions;
a) How many runs will you produce in the first pass?
b) To sort the entire file, how many passes do you need?
c) How much is involved in terms of I/O cost to sort the file?
d) If you like to sort the file in just two passes, then what is the number of buffer pages you need?

a) If Nf is the number of file pages and Nb is the number of available buffer pages then the first pass requires Nf/Nb [ceiling(Nf/Nb)] sorted runs.
For our case,
Number of file pages, Nf = 150000
Number of available buffer pages, Nb = 45
The number of sorted runs in the first pass = ⌈150000/45⌉ = 3334 runs

b) The number of passes required to sort the entire file can be calculated using the equation ⌈logNb-1Nf/Nb⌉⌉+1.
Number of passes to sort complete file = ⌈log2⌈150000/45⌉⌉+1
                                                                   = ⌈log23334⌉+1 = 13 passes

c) Since each page is read and written once per pass, the total number of page I/Os for sorting the file is 2 * Nf * (#passes):
Total I/O cost for sorting the file = 2 * 150000 * 13 = 39,00,000

d) In Pass 0, Nf/Nbruns are produced. In Pass 1, we must be able to merge this many runs; i.e., Nb − 1 ≥ Nf/Nb. This implies that Nb must at least be large enough to satisfy Nb * (Nb − 1) ≥ Nf; this can be used to guess at Nb, and the guess must be validated by checking the first inequality. Thus;
With 150000 pages in the file, Nb = 388 satisfies both inequalities, but Nb = 387 does not. So we need 388 buffer pages to sort the entire file in just two passes.
[Note: to find the value of Nb, factorize the equation Nb * (Nb-1) = Nf which can be written as a quadratic equation Nb2-Nb-Nf = 0. The equation to be solved is Nb2 - Nb - 8500 = 0]


buffer pages required for external sorting
number of passes required to complete sorting of a file using external sorting
external sorting technique in database 
number of runs required for each pass in external sorting
I/O cost involved in sorting the entire file

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