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I am trying to understand an example in Chapter 12 (Query Processing) of Database System Concepts, Sixth Edition.

A relation does not need recursive partitioning if M > nh +1, or equivalently M > (bs/M) + 1, which simplifies (approximately) to M > √ bs .

For example, consider a memory size of 12 megabytes, divided into 4-kilobyte blocks; it would contain a total of 3K (3072) blocks. We can use a memory of this size to partition relations of size up to 3K ∗ 3K blocks, which is 36 gigabytes.

How did they get to 36 gigabytes?

Also I appreciate if you could help me understand the next example.

Similarly, a relation of size 1 gigabyte requires just over √ 256K blocks, or 2 megabytes, to avoid recursive partitioning.

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3K * 3K * 4 kB = 3072 * 3072 * 4096 B = 38,654,705,664 B = 36 GB

You should now be able to do the math for the second example.

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