[DMDB] Notes on query processing, better summary for those, some exam notes

semester4/dmdb/parts/04_query-processing/01_selection/00_intro.tex

@@ -1,6 +1,7 @@
 Two terms important here are \textit{logical selection}, which describes \bi{what} we want to select and \textit{physical selection},
 which describes \bi{how} the algorithm or procedure works that actually retrieves, or filters, the data.
 
-The options include an \textit{file scan}, where we scan the entire file and thus the I/O cost is \cost{$N$}, where $N$ is the number of pages in each relation.
+The options include an \textit{file scan}, where we scan the entire file and thus the I/O cost is \cost{$N \div P_F$},
+where $N$ is the number of records in the relation and $P_F$ the number of records per page.
 Alternatively, we can use \textit{index scan}, where we use an index to retrieve the matching rows.
 The cost then of course depends on the index used and if said index can even be used to generate the resulsts needed. We will cover that in more detail now.

semester4/dmdb/parts/04_query-processing/01_selection/01_index-scan.tex

@@ -1,12 +1,19 @@
 \subsubsection{Index Scan}
 \begin{itemize}
     \item \bi{Hash Index}: {\color{ForestGreen} $\tco{1}$, we read the bucket and possibly the overflow buckets.} {\color{red} Can only be used for equality predicates}
-    \item \bi{B+ Tree Index}: $\tco{\log_F(N) + X}$, with $F$ fanout, $N$ the number of leaf nodes and $X$ the ratio of number of selected tuples and tuples per page.
-              {\color{red} $X$ can be up to 1 per selected tuple with an unclustered index}. Optimization: we could sort the RIDs.
+    \item \bi{B+ Tree Index}: $\tco{\log_F(N) + X}$ (or simply $\tco{h + X}$, with $h$ the height of the tree),
+          with $F$ fanout, $N$ the number of leaf nodes and $X$ the ratio of number of selected tuples and tuples per page.
+              {\color{red} $X$ can be up to 1 per selected tuple with an unclustered index, thus $N$ for all}. Optimization: we could sort the RIDs.
     \item \bi{Bitmap Index}: $\tco{\text{size of bitmap index}} + X$, {\color{red} $X$ depends on clustering again}
 \end{itemize}
 
-The I/O cost for B+ Tree Index Scan is \cost{$\texttt{tree height} + \texttt{\#leaf pages} + \texttt{\#file pages}$}
+The I/O cost for B+ Tree Index Scan is \cost{$\texttt{tree height} + \texttt{\#leaf pages} + \texttt{\#file pages}$}.
+Note that the number of leaf pages and file pages are multiplied with the selectivity of the predicate and are given by
+(for $\texttt{cnt}(R') = \texttt{cnt}(R) \cdot S$, with $S$ the selectivity of the predicate):
+\begin{itemize}
+    \item \texttt{\#leaf pages}: $\texttt{cnt}(R') \div (P_L \cdot F_L)$, with $P_L$ the \#records per leaf page and $F_L$ the fill factor for the leaf.
+    \item \texttt{\#file pages}: $\texttt{cnt}(R') \div P_F$, with $P_F$ the number of records per file page.
+\end{itemize}
 
 \inlineexample{Computation example}
 Given a relation $R$ with $N =$ one million records. There are 100 records on a page and we have a B+ Tree with the data entries $<k, rid>$
@@ -17,6 +24,6 @@ Then the cost is computed as follows:
     \item 3 internal nodes to parse, $\ceil{\log_F(N)}$
     \item Number of result records = $1,000,000 * 1\% = 10,000$ (this is the selectivity)
     \item Number of leaf pages pointing to the results records = $10,000 / (500 \cdot 0.67) = 30$
-    \item Number of pages in the heap file that hold the result records $= 10,000 / 100 = 30$
+    \item Number of pages in the heap file that hold the result records $= 10,000 / 100 = 100$
 \end{itemize}
 Then, the total cost is $3 + 30 + 100 = 133$