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Polyglot Persistence

The practice of using multiple database technologies within a single application, each optimized for specific data needs.
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The statement of the theorem

Let M={M1,M2,…,Mk}\mathcal{M} = \{\mathcal{M}_1, \mathcal{M}_2, \dots, \mathcal{M}_k\} be a finite set of data models (e.g., Document, Graph, Key-Value). Given a set of required access patterns P={p1,p2,…,pm}\mathcal{P} = \{\mathbf{p}_1, \mathbf{p}_2, \dots, \mathbf{p}_m\}, where each pi\mathbf{p}_i specifies a query type and associated data relationships. Define the optimal persistence strategy S:P→M\mathcal{S}: \mathcal{P} \to \mathcal{M} such that for every pi∈P\mathbf{p}_i \in \mathcal{P}, the selected model Mopt=S(pi)\mathcal{M}_{\text{opt}} = \mathcal{S}(\mathbf{p}_i) minimizes the cost function C(pi,Mopt)C(\mathbf{p}_i, \mathcal{M}_{\text{opt}}), where CC quantifies the efficiency of executing pi\mathbf{p}_i within Mopt\mathcal{M}_{\text{opt}} relative to other models Mj∈M\mathcal{M}_j \in \mathcal{M}. The goal is to find S\mathcal{S} such that ∑i=1mC(pi,S(pi))\sum_{i=1}^{m} C(\mathbf{p}_i, \mathcal{S}(\mathbf{p}_i)) is minimized.