# An Approach to Aid Decision-Making by Solving Complex Optimization Problems Using SQL Queries
## 3 Experimental Design and Results
### Second Experiment: Other Problems
#### 3.2.1 Case of Study: Special Community Network Problem  
This section presents another case of study to demonstrate that the use of SQL queries can be helpful in the solution of problems found in the analysis of data related to a research community. Remarkably, the problem consists of identifying self-referencing groups in a research community. Scientometrics is concerned with measuring and analyzing science, technology, and innovation data. One application in this area is derived from the solution to the MCP; it consists of identifying groups that intentionally or unintentionally reference each other in articles in a research community. For this purpose, it is required to identify all pairs of references between members in a research community, i.e., identifying a CLIQUE in the organization of the references between authors. To show an example, let us take the database described as follows. Let us suppose that the information relating to the articles published by a research community in a set of journals and their citations is organized in a database with the tables shown in Table 4. This database organizes the core data required to describe a publication derived from a journal or conference, i.e., the name of its publisher, address, articles, and citations. Then, self-referencing groups can be seen as groups in which all their members refer to each other in their articles, i.e., a set of authors that can be identified as referencing other members in their publications. We can model it as a CLIQUE problem to find such groups and their cardinality (the number of members who form the group). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**(a)** & **(b)** & **(c)** & **(d)** \\ \hline
**Journals** & **Articles** & **Authors** & **Citations** \\ \hline id\_journal & id\_article & id\_author & id\_journal \\ name & title & name & id\_article \\ publisher & id\_author & affiliation & cited\_by \\ address & id\_journal & & year\_cited \\  & year & & \\  & volume & pages & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Typical organization scheme for database tables that contain the publishing information of the articles in a set of journals. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Problem** & **Instance** & **Brute Force Solver** & **SQL Approach** \\ \hline PSP & \begin{tabular}{c} Securities = 10, \\ \(Q=5000\), \\ \(U(0,50,000)\) \\ Securities = 20, \\ \(Q=10,000\), \\ \(U(0,50,000)\) \\ Securities = 30, \\ PSP & \begin{tabular}{c} \(Q=15,000\), \\ \(U(0,50,000)\) \\ Securities = 40, \\ \(U(0,50,000)\) \\ \(U(0,50,000)\) \\ \end{tabular} & 0.02 & 0.01 \\ PSP & \begin{tabular}{c} \(Q=10,000\), \\ \(U(0,50,000)\) \\ Securities = 30, \\ \(U(0,50,000)\) \\ \end{tabular} & 4.27 & 0.65 \\ PSP & \begin{tabular}{c} \(Q=15,000\), \\ \(U(0,50,000)\) \\ \end{tabular} & 4743.36 & 0.11 \\ PSP & \
\begin{tabular}{c} \(Q=20,000\), \\ \(U(0,50,000)\) \\ \end{tabular} & Unsolved & 903 \\ PSP &
\begin{tabular}{c} \(N=20\), \(M=30\) \\ \(N=30\), \(M=60\) \\ \end{tabular} & 2.74 & 4.12 \\ \hline
3 CG &
\begin{tabular}{c} \(N=20,M=30\) \\ \(N=30,M=60\) \\ \(N=40\), \(M=125\) \\ \end{tabular} & 2336.26 & 36.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time in seconds spent by brute force strategies and SQL approaches in different instances. Firstly, let us consider the graph \(G=(V,E)\) formed by the set of nodes \(V\), where each node represents a different author in the database. This graph will contain an edge \((v_{i},v_{j})\) if the author \(i\) has at least one article in which he/she has cited one article of author \(j\) and author \(j\) also has at least one article in which he/she has cited author \(i\). Then, the solution of the MCP on graph \(G\) will yield a self-referencing group, and the cardinality of such a group will be its size. The SQL statement presented in Figure 4 can be used to construct the graph \(G\) from a database as the one described previously. Figure 4a presents the identification of all the pairs \((i,j)\), i.e., author \(i\) has been cited by author \(j\).