Finish 'Background and motivation'

Author: Gerold103

inconsistent_example.pdf

@@ -1,6 +1,15 @@
 \relax 
 \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
 \@writefile{toc}{\contentsline {section}{\numberline {2}Background and motivation}{1}}
+\citation{kai:slimdb}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces LSM-tree ranges dump and compaction}}{2}}
+\newlabel{fig:compaction_schema}{{1}{2}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Compaction}{2}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}LSM-tree based table structure}{2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces LSM-tree based table inconsistency example}}{2}}
+\newlabel{fig:inconsistent_example}{{2}{2}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Multiple indexes update problem}{2}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Math Equations}{2}}
 \citation{Lamport:LaTeX}
 \citation{bowman:reasoning}
 \citation{clark:pct}
@@ -11,35 +20,32 @@
 \citation{Lamport:LaTeX}
 \citation{Lamport:LaTeX}
 \citation{Lamport:LaTeX}
-\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces LSM-tree ranges dump and compaction}}{2}}
-\newlabel{fig:compaction_schema}{{1}{2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Compaction}{2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Math Equations}{2}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.1}Inline (In-text) Equations}{2}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.2}Display Equations}{2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Citations}{2}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Tables}{2}}
-\citation{salas:calculus}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}Inline (In-text) Equations}{3}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.2}Display Equations}{3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Citations}{3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Tables}{3}}
 \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Frequency of Special Characters}}{3}}
-\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A sample black and white graphic (.pdf format).}}{3}}
-\newlabel{fig:fly}{{2}{3}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Figures}{3}}
-\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces A sample black and white graphic (.pdf format) that has been resized with the \texttt  {includegraphics} command.}}{3}}
-\newlabel{fig:bigfly}{{3}{3}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Theorem-like Constructs}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces A sample black and white graphic (.pdf format).}}{3}}
+\newlabel{fig:fly}{{3}{3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Figures}{3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces A sample black and white graphic (.pdf format) that has been resized with the \texttt  {includegraphics} command.}}{3}}
+\newlabel{fig:bigfly}{{4}{3}}
+\citation{salas:calculus}
 \bibstyle{abbrv}
 \bibdata{vldb_sample}
 \bibcite{bowman:reasoning}{1}
 \bibcite{braams:babel}{2}
 \bibcite{clark:pct}{3}
 \bibcite{herlihy:methodology}{4}
 \bibcite{Lamport:LaTeX}{5}
-\bibcite{salas:calculus}{6}
+\bibcite{kai:slimdb}{6}
+\bibcite{salas:calculus}{7}
 \@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Some Typical Commands}}{4}}
-\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces A sample black and white graphic (.pdf format) that needs to span two columns of text.}}{4}}
-\newlabel{fig:flies}{{4}{4}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.8}Theorem-like Constructs}{4}}
 \@writefile{toc}{\contentsline {section}{\numberline {3}Conclusions}{4}}
 \@writefile{toc}{\contentsline {section}{\numberline {4}Acknowledgments}{4}}
 \@writefile{toc}{\contentsline {section}{\numberline {5}References}{4}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}References}{4}}
-\@writefile{toc}{\contentsline {section}{\numberline {A}Final Thoughts on Good Layout}{4}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces A sample black and white graphic (.pdf format) that needs to span two columns of text.}}{5}}
+\newlabel{fig:flies}{{5}{5}}
+\@writefile{toc}{\contentsline {section}{\numberline {A}Final Thoughts on Good Layout}{5}}

inconsistent_example.psd

@@ -1,3 +1,12 @@
+@INPROCEEDINGS{kai:slimdb,
+	AUTHOR = "Kai Ren and Qing Zheng and Joy Arulraj and Garth Gibson",
+	TITLE = "SlimDB: A Space-Efficient Key-Value Storage Engine For Semi-Sorted Data",
+	BOOKTITLE = "Proceedings of the VLDB Endowment",
+	ORGANIZATION = "VLDB Endowment",
+	MONTH = "August",
+	YEAR = {2017},
+	VOLUME = "{10}"	}
+
 @ARTICLE{bowman:reasoning,
 	AUTHOR = "Mic Bowman and Saumya K. Debray and Larry L. Peterson",
 	TITLE = "Reasoning About Naming Systems",

vldb_sample.aux

@@ -300,6 +300,57 @@ \subsection{Compaction}
 key values into ranges, when each range stores and maintains its own sublevels
 independently of other ranges (see Figure \ref{fig:compaction_schema}).
 
+\subsection{LSM-tree based table structure}
+In LSM-tree based table each index is an LSM-tree, sorted by the index parts.
+It is common pattern, that a table has one primary index and a number of
+secondary indexes. A primary index always is unique, and stores full tuples,
+including all indexed and not indexed fields, as they were inserted by an user.
+A secondary index stores only its own key parts and primary index parts to save
+memory. Such indexes are called non-covering. Primary parts are used as link to
+a full tuple in a primary index, when a search uses a secondary index only.
+
+The described pattern is not unique feature of LSM-tree based tables. For
+example, SQLite secondary indexes based on B-tree are not covering by default
+too. And each SQLite table has unique primary index even if an user did not
+specified it explicitly.
+
+Since secondary indexes stores primary index parts, they are linked with primary
+indexes. And if a tuple does not exist in a primary index, the same tuple can
+not exist in a secondary index. This is the reason, why hidden reads are
+indispensible - if a tuple is replaced with another secondary key or deleted
+from a primary index, then its old version must be deleted from each secondary
+index by old secondary key, else a table indexes are not consistent.
+
+\subsection{Multiple indexes update problem}
+LSM-tree ability to manage multiple versions of a key allows to avoid hidden
+reads on such operations as replace or delete which can not break consistency if
+there is only a primary index in a table and no foreign key constraints.
+Such operations are known as \textbf{blind-writes} \cite{kai:slimdb}.
+Blind-writes are much faster than non-blind insert or update operations, which
+read an old tuple in a worst case from a disk to check for duplicate or apply
+update operations.
+
+The big problem of LSM-tree based tables is that in presense of secondary
+indexes all writes become non-blind. See Figure \ref{fig:inconsistent_example}
+for example of inconsistency if replace is blind and a table has secondary
+index. Here a table is defined with 4 columns: first is part of a primary index,
+2 and 3 are parts of a secondary index, and 4 is not indexed.
+\textit{Replace\{1, 5, 6, 7\}} before executed must read old tuple from a
+primary index by the key \textit{\{1\}}, extract the secondary key
+\textit{\{2, 3\}}, delete it from the secondary index, and only then insert the
+new tuple. If the old tuple is not deleted, then during compaction it becames
+garbage with no link to a full tuple in the primary index.
+\begin{figure}
+\centering
+\includegraphics[width=0.3\textwidth]{inconsistent_example}
+\caption{LSM-tree based table inconsistency example}
+\label{fig:inconsistent_example}
+\end{figure}
+
+Since disk access is much slower than memory access, secondary index presence
+destroys LSM-tree versions advantage. In the next section a new LSM-tree update
+algorithm is presented reviving versions and blind-writes.
+
 \subsection{Math Equations}
 You may want to display math equations in three distinct styles:
 inline, numbered or non-numbered display.  Each of