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\title{"Globally Recorded binary encoded Domain Compression algorithm in Column Oriented Databases"}
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\begin{document}

             \author[1]{Mehul Mahrishi  }

             \author[2]{Anita  Shrotriya}

             \author[3]{Devendra Kr.  Sharma}

             \affil[1]{  }

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\date{\small \em Received: 17 November 2011 Accepted: 13 December 2011 Published: 24 December 2011}

\maketitle


\begin{abstract}
        


through this study, we propose two algorithms. The first algorithm describes the concept of compression of domains at attribute level and we call it as ?Attribute Domain Compression?. This algorithm can be implemented on both row and columnar databases. The idea behind the algorithm is to reduce the size of large databases as to store them optimally. The second algorithm is also applicable for both concepts of databases but will optimally work for columnar databases. The idea behind the algorithm is to generalize the tuple domains by giving it a value say (n) such that all other n-1 tuples or at least maximum can be identified.

\end{abstract}


\keywords{Compression, Columnar database, tuples, tables.}

\begin{textblock*}{18cm}(1cm,1cm) % {block width} (coords) 
\textcolor{GJBlue}{\LARGE Global Journals \LaTeX\ JournalKaleidoscope\texttrademark}
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\textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}}
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\let\tabcellsep& 	 	 		 
\section[{INTRODUCTION}]{INTRODUCTION}\par
ill now we have studied that a database is a collection of inter-related data which is organized in a matrix with rows and columns. Each column represents the attribute of that particular entity which is converted into the database table, while each row of the matrix generally called a tuple represents the different values that an attribute can possess. Each row in a table represents a set of related data, and every row in the table has the same structure.\par
For example, in a table that represents employee, each row would represent a single employee. Columns might represent things like employee name, employee street address, his SSN etc. In a table that represents the relationship of employees with departments, each row would relate one employee with one department.  
\section[{RISE OF COLUMN DATABASE}]{RISE OF COLUMN DATABASE}\par
The relational databases present today are designed predominantly to handle online transactional processing (OLTP) applications. A transaction (e.g. an online purchasing a laptop through internet dealer) typically maps to one or more rows in a relational database, and all traditional RDBMS designs are based on a per row paradigm. For transactional-based systems, this architecture is well suited to handle the input of incoming data.\par
Data warehouses are used in almost every large organizations and research states that their size doubles after every third year. Moreover the hourly workload of these warehouses is huge and approximately 20lakhs SQL statements are encountered hourly.\par
Warehouses contain a lot of data and hence any leak or illegal publication of information risks the individuals' privacy. However, for applications that are very read intensive and selective in the information being requested, the OLTP database design isn't a model that typically holds up well. Business intelligence and analytical applications queries often analyze selected attributes in a database. The simplicity and performance characteristic of columnar approach provides a cost effective implementation.\par
Column oriented database generally known as "columnar database" reinvents how data is stored in databases. Storing data in such a fashion increases the probability of storing adjacent records on disk and hence odds of compression. This architecture suggests a different model in which inserting and deleting transactional data are done by a row-based system, but selective queries that are only interested in a few columns of a table are handled by columnar approach.\par
As we know that logical and critical queries requires more number of rows that that of physical I/O queries which are comparatively slower queries, the performance gap between row-oriented architectures and column-oriented architecture oftentimes widens as the database grows.\par
Different methodologies such as indexing, materialistic views, horizontal partitioning etc. are provided by row oriented databases which are rather Global Journal of Computer Science and Technology Volume XI Issue XXIII Version I 27 better ways of query execution, but they also have some disadvantages of their own. For example, in business intelligence/analytic environments, the ad-hoc nature of such scenarios makes it nearly impossible to predict which columns will need indexing, so tables end up either being over-indexed (which causes load and maintenance issues) or not properly indexed and so many queries end up running much slower than desired. 
\section[{III. ANONYMIZATION}]{III. ANONYMIZATION}\par
Warehouses contain a lot of data and hence any leak or illegal publication of information risks the individuals' privacy. N-Anonymity is a major technique to deidentify a data set. The idea behind the technique is to determine the value of a tuple, say n, such that other remaining n-1 tuples or at least maximum tuples can be identified by the value of n.\par
The intensity of protection increases with increase the number of n. One way to produce n identical tuples within the identifiable attributes is to generalize values within the attributes, for example, removing city and street information in a address attribute.\par
There are many ways through which data unidentification can be done and one of the most appropriate approaches is generalization. Various generalization techniques include global recoding generalization multidimensional recoding generalization, and local recoding generalization. Global recoding generalization maps the current domain of an attribute to a more general domain. For example, ages are mapped from years to 10-year intervals.\par
Multidimensional recoding generalization maps a set of values to another set of values, some or all of which are more general than the corresponding premapping values. For example, \{male, 32, divorce\} is mapped to \{male, [30, 40), unknown\}. Local recoding generalization modifies some values in one or more attributes to values in more general domains. 
\section[{IV. PROBLEM DEFINITION AND CONTRIBUTION}]{IV. PROBLEM DEFINITION AND CONTRIBUTION}\par
From the very beginning we have cleared that our objective is to make every tuple of a published table identical to at least n-1 other tuples. Identity-related attributes are those which potentially identify individuals in a table. For example, the record of an old-aged male in the rural area with the postcode of 302033 is unique in Table \hyperref[tab_1]{4}.1, and hence, his problem of asthma may be revealed if the table is published. To preserve his privacy, we may generalize Gender and Postcode attribute values such that each tuple in attribute set \{Gender, Age, Postcode\} has at least two occurrences.  
\section[{QUALITY MEASURES OF ANONYMIZATION}]{QUALITY MEASURES OF ANONYMIZATION}\par
After the study we can easily conclude that larger the size of equivalent set easier the compression and obviously cost of anonymization is a factor of equivalent set. On the basis of this theory, we can determine that:( ) ? ? = ? 
\section[{RECORDS CAVG}]{RECORDS CAVG} 
\section[{VI. DOMAIN COMPRESSION THROUGH BINARY CONVERSION}]{VI. DOMAIN COMPRESSION THROUGH BINARY CONVERSION}\par
We integrate two key methods, namely binary encoding of distinct values and pair wise encoding of attributes, to build our compression technique. 
\section[{a) Encoding of Distinct values}]{a) Encoding of Distinct values}\par
This compression technique is based on the assumption that the table we have published contains minimum distinct domain of attributes and these values repeat over the huge number of tuples present in the database. Therefore, binary encoding of the distinct values of each attribute, followed by representation of the tuple values in each column of the relation with the corresponding encoded values would transform the entire relation into bits and thus compress it.\par
We will find out the number of distinct values in each column and encode the data into bits accordingly. For example consider an instant given below which represents the two major attributes of a relation Patients. To examine the compression benefits achieved by this method assume that Age is of integer type and has 5 distinct values as in Table \hyperref[tab_1]{4}.3. Suppose if there are 50 patients then the total storage required by Age attribute will be 50*size of (int) = 50*4 = 200 bytes.\par
With our compression technique, we find that there are 9 distinct values for age therefore we need the upper bound of log (9) i.e. 4 bits to represent each data value in the Age field. It is easy to calculate that we would need 50*4 (bits) = 200 bits = 25 bytes which are reasonably less.\par
We call this as our stage 1 of our compression which just transforms one column into bits. If we apply this compression to all columns of the table, the result will be significant. It can be easily seen from the above example that besides optimizing the memory requirement of the relations, above encoding technique is also helpful in reducing redundancy (repetition values) from the relation. That is, it is likely that they are few distinct values of even (column1, column2) taken together, in addition to just column1's distinct values or column2's distinct values. We then represent the two columns together as a single column with pair values transformed according to the encoding. This constitutes Stage 2 of our compression in which we use the bit-encoded database from Stage 1 as input and further compress it by coupling columns in pairs of two, applying the distinct-pairs technique outlined. To examine the further compression advantage achieved, suppose that we couple 'Age' and 'Problem' columns. We can see in our table \hyperref[tab_1]{4}.3 that there are 5 distinct pairs (10, Cough \& Cold), (20, cough \& cold), (30, obesity), (50, Diabetes), (70, Asthma) and hence our upper bound is log (5) = 2 bits approx. Table \hyperref[tab_1]{4}.6 shows the result of stage 2 compression. After compressing the attribute, pairing or coupling of attributes is done. All the columns are coupled in pair of two in a similar manner. If the database contains even number of columns it is straightforward. If the columns are odd, we can intelligently choose any of the columns to be uncompressed. The second technique focuses on the extension of existing compression by encoding the domain in binary form and further encoding pairs of column values. It shows how coupling of columns can be effective if attributes are properly rearranged. In particular I found that in most cases it is beneficial to couple the primary key with the column having the maximum number of distinct values. Also, columns with very few distinct values should be paired with columns with a large number of dissimilar values. Functional dependencies should be determined to achieve better compression of related attributes. Overall, a better knowledge of the data distribution leads to better compression. Based on the database and the application environment being targeted, the optimum stage up to which compression is feasible and worthy also needs to be determined, i.e. we need to decide the point at which the extra compression achieved is not worth the performance overhead involved.\begin{figure}[htbp]
\noindent\textbf{2011}\includegraphics[]{image-2.png}
\caption{\label{fig_0}T © 2011}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.6194915254237288\textwidth}P{0.1152542372881356\textwidth}P{0.1152542372881356\textwidth}}
\multicolumn{3}{l}{1 : a Typical Row oriented Database}\\
Column 1\tabcellsep Column 2\tabcellsep Column 3\end{longtable} \par
 
\caption{\label{tab_0}Table 2 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.5193292682926829\textwidth}P{0.1378658536585366\textwidth}P{0.06323170731707317\textwidth}P{0.07048780487804879\textwidth}P{0.05908536585365854\textwidth}}
\tabcellsep \tabcellsep \multicolumn{2}{l}{1 : Published Table}\tabcellsep \\
No.\tabcellsep Gender\tabcellsep Age\tabcellsep Postcode\tabcellsep Problem\\
01\tabcellsep Male\tabcellsep Young\tabcellsep 302020\tabcellsep Heart\\
02\tabcellsep Male\tabcellsep Old\tabcellsep 302033\tabcellsep Asthma\\
03\tabcellsep Female\tabcellsep Young\tabcellsep 302015\tabcellsep Obesity\\
04\tabcellsep Female\tabcellsep Young\tabcellsep 302015\tabcellsep Obesity\\
\multicolumn{5}{l}{Table 4.2 : View of published table by Global recording}\\
\multicolumn{2}{l}{No. Gender}\tabcellsep Age\tabcellsep \multicolumn{2}{l}{Postcode Problem}\\
01\tabcellsep *\tabcellsep Young\tabcellsep 3020*\tabcellsep Heart\\
02\tabcellsep *\tabcellsep Old\tabcellsep 3020*\tabcellsep Asthma\\
03\tabcellsep *\tabcellsep Young\tabcellsep 3020*\tabcellsep Obesity\\
04\tabcellsep *\tabcellsep Young\tabcellsep 3020*\tabcellsep Obesity\\
\tabcellsep \multicolumn{4}{l}{A view after this generalization is given in Table}\\
\multicolumn{5}{l}{4.2. Since various countries use different postcode}\\
\multicolumn{5}{l}{schemes, we adopt a simplified postcode scheme,}\\
\multicolumn{5}{l}{where its hierarchy \{302033, 3020*, 30**, 3***, *\}}\\
\multicolumn{5}{l}{corresponds to \{rural, city, region, state, unknown\},}\\
\multicolumn{2}{l}{respectively.}\tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{3}{l}{a) Identifier attribute set}\tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{4}{l}{A set of attributes that potentially identifies the}\\
\multicolumn{5}{l}{individuals in a table is a set of identifier attribute. For}\\
\multicolumn{5}{l}{example, attribute set \{Gender, Age, Postcode\} in Table}\\
\multicolumn{3}{l}{1a is an identifier attribute set.}\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{b) Equivalent Set (?)}\tabcellsep \tabcellsep \\
\tabcellsep V.\tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}Table 4 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.6928082191780822\textwidth}P{0.1571917808219178\textwidth}}
Age\tabcellsep Problem\\
10\tabcellsep Cough \& Cold\\
20\tabcellsep Cough \& Cold\\
30\tabcellsep Obesity\\
50\tabcellsep Diabetes\\
70\tabcellsep Asthma\\
\multicolumn{2}{l}{Now if we adopt the concept of N-}\\
\multicolumn{2}{l}{Anonymization with global recording (refer 4.2), we can}\\
\multicolumn{2}{l}{map the current domain of attributes to more general}\\
\multicolumn{2}{l}{domain. For example Age can be mapped into 10-Age}\\
\multicolumn{2}{l}{interval as shown in the figure 4.4.}\end{longtable} \par
 
\caption{\label{tab_2}Table 4 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.6443548387096774\textwidth}P{0.2056451612903226\textwidth}}
\multicolumn{2}{l}{6 : Representing Stage 2 compression}\\
Age\tabcellsep Problem\\
00\tabcellsep 00\\
01\tabcellsep 01\\
10\tabcellsep 10\\
11\tabcellsep 11\end{longtable} \par
 
\caption{\label{tab_3}Table 4 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.85\textwidth}}
7 : Representing Stage 2 compression coupling\\
Age-Problem\\
00\\
01\\
10\\
11\\
After this compression technique is applied we\\
can easily calculate the space required i.e.\\
Before compression: 5*(4) +4*(4) = 36 bytes\\
After Compression and coupling: 4*2 = 8 bits.\\
VII. CONCLUSION\\
In this study we discuss two different\\
compression techniques embedded with each other to\\
form a "Globally Recorded binary encoded Domain\\
Compression".\\
The first study defines generalization and\\
discuss its different type in anonymization the attributes.\\
It discusses how to handle a major problem in global\\
recoding generalization, inconsistent domains in a field\\
of a generalized table, and propose a method to\\
approach the problem. The tables in the examples\\
proposed global recoding method based on n-\\
anonymity, and consistency.\end{longtable} \par
 
\caption{\label{tab_4}Table 4 .}\end{figure}
 			\footnote{December} 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXIII Version I} 			\footnote{December"Globally Recorded binary encoded Domain Compression algorithm in Column Oriented Databases"} 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XXIII Version I 29 2011 December "Globally Recorded binary encoded Domain Compression algorithm in Column Oriented Databases"} 			\footnote{December"Globally Recorded binary encoded Domain Compression algorithm in Column Oriented Databases"} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}
