DBMS solved exercises, database query processing and optimization solved exercises, how to find the query IO cost for natural join

__Question:__

Consider doing a natural join operation on two relations R(A, B) and S(B, C). Assume that the tuples of R are stored contiguously on 400 disk blocks, while the tuples of S are stored contiguously on 1000 blocks. Each block holds 20 tuples (same for R as for S). There are 51 memory blocks available.

Calculate the I/O cost for iteration join (assume that R and S are not sorted), and sort-merge join (assume that R and S are sorted on attribute B) algorithms. Ignore the I/O cost of writing the final output to disk.

__Solution:__

Given,

Total disk blocks for R, B(R) = 400

Total disk block for S, B(S) = 1000

__Iteration join:__

We have only 51 blocks are available in main memory. The iteration join algorithm can read 50 R blocks into memory, and all blocks of S (1 block at a time) into memory at a time, to join S with R. The process is repeated until all outputs are generated.

Number of IOs to read R into memory = 400, (ie., 50 * 8)

Number of IOs to read S into memory = for each of 50 R blocks we need 1000 IOs to read S

Total number of IOs required = 400 + 1000 * 8 = 8400

__Merge join:__

Given,

Both R and S are sorted on the join attribute B.

__Merge
join__*: Both sorted files are scanned
concurrently in order of the join attributes, matching the records that have
the same values for A and B.*

Cost of merging R and S = B(R) + B(S) = 400 + 1000 = 1400

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