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eth-summaries/semester4/dmdb/parts/04_query-processing/04_join/01_nested-loops.tex
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\subsubsection{Nested Loops Join (NLJ)}
\begin{algorithm}
\caption{Nested Loops Join Algorithm}
\begin{algorithmic}[1]
\Procedure{NestedLoopsJoin}{$R$, $S$}
\For{each page $p_R \in R$}
\For{each page $p_S \in S$}
\State Join the tuples on page $p_R$ with the tuples on page $p_S$ (evaluate the predicate for all pairs)
\State Add matching tuples to the join output
\EndFor
\EndFor
\EndProcedure
\end{algorithmic}
\end{algorithm}
The cost here is \cost{$P_R + P_R \cdot P_S$ I/Os}, where $P_X$ is the number of pages in the relation $X$.
Furthermore, the DBMS should put the smaller relation on the outer loop to improve performance.