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[DMDB] Fix issues, improve query processing with notes on time complexities
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@@ -16,7 +16,7 @@
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We have $B$ buffer frames, of which one is reserved for the pages of $S$ and one is reserved for the output, thus the $B - 2$ blocks.
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Each of these blocks houses $P_R / (B - 2))$ pages of $R$, reducing search costs by only scanning $S$ once for every block.
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The cost here is $P_R + (P_R / (B - 2) \cdot P_S$ I/Os.
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The cost here is \cost{$P_R + (P_R / (B - 2) \cdot P_S$ I/Os}.
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If however, $R$ fits into memory, we have cost $P_R + P_S$ I/Os.
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We can reduce that further by building as second step (right after the first for loop) a in-memory hash table for the tuples in the $R$ pages block.
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This reduces the cost of comparisons, however, we need $(B - 2) \cdot f$ memory now.
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