## 3 Proposed Methodology
### _Rfo-Svm_
#### 3.5.2 Data Fragmentation  
The classified data are divided into fragments and each fragment contains a subset of the original data that belongs to a predicate set \(\psi=\left[\psi_{1},\ldots\psi_{p}\right]\) and these predicates are assigned to all attributes \((N_{a})\), i.e., \(X[X_{1},\ldots,X_{n}]\). The numerical attributes are assumed to possess one of 3 states \(\left(\psi_{j}>value\ 1\right)\), \(\psi_{i}<value\ 2)\) or \(\psi_{i}=value\ 3)\). The alphabetical attributes are assigned to have a single state value \(\left[\psi_{i}=\alpha\right]\). For all predicates, the retrieval and frequencies are updated for each attribute and are provided by the database administrator in the form of \(\left(\psi_{i}\cdot Q_{Rf}\right)\) and \(\psi_{i}\cdot Q_{Uf}\). The most frequently used queries \((Q_{S})\) require attributes that are continuously observed and released from several sites and each query possess its own query frequency \(\frac{Q_{Rf}}{Q_{Uf}}\) in each site over data. The queries \((Q_{S})\) from several sites (M) are treated as different queries in each site with \(\frac{Q_{Rf}}{Q_{Uf}}\) frequency. The query frequency matrix \(\left(Q_{fm}\right)\) saves these frequencies exactly. The proposed architecture is depicted in Figure 2 with the following explanation:  
* The relations that are being considered are expected to be defined and recognized. * All frequently used queries that are consistently observed to access each relation, regardless of their type (retrieval or update), are retained and individually considered. The frequencies of these queries over sites, as well as the retrieval and update frequencies of queries over data in all sites, are meticulously taken in \(Q_{f}\), \(Q_{R}\), and \(Q_{U}\) matrices, respectively. Data fragmentation is initiated using these matrices in conjunction with the fragmentation cost model. * By utilizing Equation (22), in conjunction with the above-mentioned matrices, Attribute Frequency Accumulation (AFAC) is hosted. * The Communication Cost Matrix \((CCM)\) is transformed into a Distance Cost Matrix \((DCM)\) using the Genetic Algorithm. Then, Equation (24) is utilized to multiply \(DCM\) by AFAC, resulting in the Total Frequencies of Attributes predicate Matrix (TFAM). * Next, TFAM is used to calculate the overall access costs for each attribute individually, yielding the total pay. All attributes will then be sorted based on their pay. * Finally, among these attributes, the attribute with the highest pay is selected as the Candidate Attribute (CA), which initiates the successful execution of the fragmentation process, as depicted in Equation (25). Objective Function: The objective function is better suitable for the specific circumstances and accurately reflects the transmission cost (TC). The first equation is used to measure the costs incurred during the processing of distributed retrieval queries, while Equation (23) measures the costs resulting from performing distributed update queries in a DDBS. \[TC_{1}=\sum_{j=1}^{m}\sum_{i=1}^{m}\sum_{k=1}^{q}\left(1-X_{kj}\right)\times Q _{Rkj}\times F_{size}\times CMS_{ij} \tag{22}\]  
\[TC_{2}=\sum_{j=1}^{m}\sum_{i=1}^{m}\sum_{k=1}^{q}\left(1-X_{kj}\right)\times Q _{Ukj}\times F_{size}\times CMS_{ij} \tag{23}\]  
\[TC_{total}=TC_{1}+TC_{2} \tag{24}\]The total transmission costs can be accurately calculated using Equation (24). The impact of the objective function is discussed below. \(TC_{1}\)_and_\(TC_{2}\) represent the transmission costs for retrieval and update operations, respectively (Equations (22) and (23)). CMS refers to the cost matrix between sites (CSM) or the cost matrix between clusters of sites (CCM). \(F_{size}\) represents the size of the considered fragment, and \(X_{ij}\) is a binary variable indicating the allocation of the fragment across sites.