From c409d74ad4864981dc70531d705c1b50263e8347 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 1 Jul 2026 14:05:20 +0200 Subject: [PATCH] [DMDB] Query optimization, basics of memory management --- semester4/dmdb/assets/db-system-memory.png | Bin 0 -> 70714 bytes .../dmdb/assets/join-ordering-example.png | Bin 0 -> 52823 bytes .../dmdb/data-modelling-databases-summary.pdf | Bin 815285 -> 958535 bytes .../01_search-space/01_rewriting-rules.tex | 66 ++++++++++++++++++ .../01_search-space/02_execution-model.tex | 31 ++++++++ .../01_search-space/03_cost-model.tex | 66 ++++++++++++++++++ .../01_search-space/04_search.tex | 36 ++++++++++ .../00_memory/00_intro.tex | 18 +++++ .../00_memory/01_blocks-pages.tex | 0 semester4/dmdb/parts/03_systems/main.tex | 13 +++- 10 files changed, 228 insertions(+), 2 deletions(-) create mode 100644 semester4/dmdb/assets/db-system-memory.png create mode 100644 semester4/dmdb/assets/join-ordering-example.png create mode 100644 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zZLSaSBnyc&8T~7(B09Ba*+VGuzPGpWWz^$lzsKC%5YTMPM5B6_kYG8> zFA0qI4Olfjxw}0P_eI#qeS%k5qrA8WoO%-3dyNMVLG-JAxyw{*8tJ#~b>_6Ovpj9G zxPb&dS-ZW0-NR>{sZvTQ(zg9ZI>ch05A%J{>J?OciKiAj4(8Gk4K=sZHX9uTn;N1H zKGl~veOj}8{Mw_>}V8UwI(E60dx80m2)qt*1F+)RLOXB^^Yp1(g1%;V&aYY z22q!(Xe(mBS>^8qOchEPhp{APtmd@frUU2phpQ7-FR`>gkDcv!cp5@V6#%OkG9yLm z;*YoVj{OkJcL0O)WHpM{)&uB9OxZ@}SVo%YJdWJkxSU-M6*v@J{EYKpSd6kK val} & $|\max(\texttt{col}) - \texttt{val}| \div (\max(\texttt{col}) - \min(\texttt{col}))$ & \texttt{col > 5} \\ + \texttt{col < val} & $|\texttt{val} - \min(\texttt{col})| \div (\max(\texttt{col}) - \min(\texttt{col}))$ & \texttt{col < 5} \\ + \texttt{col1 = col2} & $1 \div \max(\#\texttt{UniqueValues(col1)}, \#\texttt{UniqueValues(col2)})$ & \texttt{t.name = s.name} \\ +\end{tables} + +This table shows the overall concept for the cardinality estimation. +For each predication, a reduction factor is determined, as each predicate ``filters'' out some tuples. + +Thus, the resulting cardinality is $\max(\#\text{tuples}) \cdot \prod_{r \in RF} r$, where $RF$ is the \gls{bag} of all reduction factors. + +In all of the above estimators, we assumed that the values are uniformly distributed. +This of course is not always true --- there are many cases where data is heavily skewed --- in which cases, histograms are used. + +Two types of histograms are commonly used: +\begin{itemize} + \item \bi{Equi-Width}: Here, the heights (tuple counts) of the buckets differ, as we fix the values for each bucket. + This is useful for identifying hot-spots. + \item \bi{Equi-Depth} (or Equi-Height): Here, the width differs, because we want all buckets to contain the same number of tuples. + The size of a range helps with cardinality estimates + \item \bi{Singleton} (or Frequency): Plots how often a single item appears in a table. + This is very useful to compute the selectivity of queries +\end{itemize} + +\newpage +To enable quick processing of the cost function, the following metadata, or statistics, are typically stored: +\begin{multicols}{2} + \bi{Table statistics} + \begin{itemize} + \item Number of rows + \item Number of blocks + \item Average row length + \end{itemize} + \bi{Column statistics} + \begin{itemize} + \item Number of distinct values (NDV) in columns + \item Number of nulls in column + \item Data distribution (histogram) + \end{itemize} + \bi{Extended statistics} + \begin{itemize} + \item Index statistics + \item Number of leaf blocks + \item Levels + \item Clustering factor + \end{itemize} + \bi{System statistics} + \begin{itemize} + \item I/O performance and utilization + \item CPU performance and utilization + \end{itemize} +\end{multicols} diff --git a/semester4/dmdb/parts/03_systems/00_query-optimization/01_search-space/04_search.tex b/semester4/dmdb/parts/03_systems/00_query-optimization/01_search-space/04_search.tex new file mode 100644 index 0000000..cc17e8c --- /dev/null +++ b/semester4/dmdb/parts/03_systems/00_query-optimization/01_search-space/04_search.tex @@ -0,0 +1,36 @@ +\subsubsection{Search} +We now know how to generate a set of semantically equivalent physical plans and how to estimate the cost for each of them. +The question that remains is how to efficiently find the best plan. + +Since real-world queries can be very complex, searching for the best physical plan can be hard. +There are a few options, but we only covered a simple approach. + +We can constrain the search space by only considering \bi{left-deep join trees}, i.e. trees that have only leafs on the right hand side of each join statement. +The rationale behind this is that many of these are fully pipelined plans and no intermediate results have to be written to temporary files. +This is the concept \texttt{System R}, the first relational database used. + +An example for a non-pipelined left-deep join tree is one in volving sort operations. +This brings the complexity down to \tco{n!}, where $n$ is the number of realations in the join. + +\begin{itemize} + \item Enumerate join orders (different left deep trees) + \item Enumerate plans for each operator (hash join, sort merge join, nested loop join, \dots) + \item Enumerate access methods for each operator (B+-Tree, hash table, sequential scan, \dots) +\end{itemize} + +This can be achieved using dynamic programming. + +We then find the best 1-relation plan, then the best 2-relation plan by finding ways to join a relation with the best 1-relation plan, etc. + +While this is still slow, it's faster than enumerating all possible join trees. + +Later, systems started introducing heuristics to reduce the number of choices that must be made in a cost-based fashion. + +Heuristic optimization transforms the query-tree using a set of rules typically improve execution performance: +\begin{itemize} + \item Perform selection early (reduces the number of tuples to process) + \item Perform projection early (reduces the number of attributes to process) + \item Perform most restrictive selection and join operations before other similar operations +\end{itemize} + +Some systems only use heuristics, while others combine them with partial cost-based optimization. diff --git a/semester4/dmdb/parts/03_systems/01_database-engines/00_memory/00_intro.tex b/semester4/dmdb/parts/03_systems/01_database-engines/00_memory/00_intro.tex new file mode 100644 index 0000000..82b041f --- /dev/null +++ b/semester4/dmdb/parts/03_systems/01_database-engines/00_memory/00_intro.tex @@ -0,0 +1,18 @@ +\subsubsection{Storage Management} +To make database engines easy to use, some abstractions have to happen. +\begin{figure}[h!] + \begin{center} + \includegraphics[width=0.7\textwidth]{assets/db-system-memory.png} + \end{center} + \caption{Overview of a typical abstraction for a database system + (Figure from lecture slides 09, slide 3)} +\end{figure} + +In the design of database engines it is commonly assumed that the data is stored on spinning disks, i.e. HDDs, with a high latency for seeks (random accesses) +and that most of the DB is not in memory. + +Very modern database systems may assume that a higher percentage of the DB is stored in memory due to the higher quantity of memory available, +as well as lower access latencies due to the more readily available SSDs and high-speed NASes. + +Some database systems operate similarly to operating systems in certain aspects, in that they manage their own processes and all of the memory +to get the absolute maximum performance out of the systems. diff --git a/semester4/dmdb/parts/03_systems/01_database-engines/00_memory/01_blocks-pages.tex b/semester4/dmdb/parts/03_systems/01_database-engines/00_memory/01_blocks-pages.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester4/dmdb/parts/03_systems/main.tex b/semester4/dmdb/parts/03_systems/main.tex index 276a34d..562bd33 100644 --- a/semester4/dmdb/parts/03_systems/main.tex +++ b/semester4/dmdb/parts/03_systems/main.tex @@ -4,5 +4,14 @@ \input{parts/03_systems/00_query-optimization/00_intro.tex} \input{parts/03_systems/00_query-optimization/01_search-space/00_basics.tex} \input{parts/03_systems/00_query-optimization/01_search-space/01_rewriting-rules.tex} -% \input{parts/03_systems/00_query-optimization/01_search-space/} -% \input{parts/03_systems/00_query-optimization/} +\input{parts/03_systems/00_query-optimization/01_search-space/02_execution-model.tex} +\input{parts/03_systems/00_query-optimization/01_search-space/03_cost-model.tex} +\input{parts/03_systems/00_query-optimization/01_search-space/04_search.tex} + +\newpage +\subsection{Database Engines} +\input{parts/03_systems/01_database-engines/00_memory/00_intro.tex} +% \input{parts/03_systems/01_database-engines/00_memory/} +% \input{parts/03_systems/01_database-engines/} + +% \input{parts/03_systems/}