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40 lines
2.0 KiB
TeX
40 lines
2.0 KiB
TeX
\newpage
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\subsection{Concurrency Control}
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The goal of concurrency control is to ensure the correct executions of concurrent transactions.
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The baseline for correctness is, as previously mentioned, serial execution.
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\inlinedefinition[Serial History] A history $H$ is serial if, for every pair of two transactions $T_i$ and $T_j$ that appear in $H$,
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either all operations from $T_i$ appear before all all operations of $T_j$, or vice versa.
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A serial history with only committed transactions is correct by definition, because transactions are isolated and each transaction starts in a consistent state
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and leaves the DB in a consistent state.
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\inlinedefinition[Equivalent History] Two histories are equivalent if and only if
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\begin{enumerate}
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\item They are over the same transactions and contain the same operations
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\item Conflicting operations of non-aborted transactions are ordered in the same way in both histories
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\end{enumerate}
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\inlinedefinition[Serializable History] A history is serializable if and only it is equivalent to a serial history.
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\inlinetheorem[Serializability] A history is serializable if and only if its serializability graph is acyclic.
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The seerializabililty graph is constructed from the history graph as follows:
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\begin{enumerate}
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\item The start node is the transaction the first operation.
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\item Then, follow the operations, adding any new transaction to the tree and connect any further dependencies.
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\end{enumerate}
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More visually, see the below graphics
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\begin{figure}[h!]
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\begin{center}
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\begin{subfigure}{0.49\textwidth}
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\includegraphics[width=0.9\textwidth]{assets/serializability-graph-history.png}
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\caption{The history}
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\end{subfigure}
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\begin{subfigure}{0.49\textwidth}
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\includegraphics[width=0.7\textwidth]{assets/serializability-graph-built.png}
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\caption{The resulting serializability graph}
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\end{subfigure}
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\end{center}
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\caption{Building a serializability graph (Figure from lecture slides 19, slide 37 and 38)}
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\end{figure}
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