HgMed: Hypergraphs Mediating Schematic Translations Between Data Models

Hypergraphs are trivial mathematical structures that can embed other data models. For instance, relations in relational models, and edges in graphs and tree data models can all be naturally represented by hyperedges. Hypergraphs into other data models are a non-trivial generalization where the translations may suffer information and semantic loss due to the richness of hypergraphs in representing complex data and complex relationships. The lossy translations may impact the representation of adequate information, as in hypergraphs. However, achieving a hypergraph-based lossless generalization is a challenge. To address this issue, this paper proposes an embedding-based hypergraph-mediated translation approach called Hypergraph Mediator or HgMed based on a high-level hypergraph data model. The HgMed involves translation patterns for schematic abstractions from hypergraphs to other models and vice versa, such that the repeated translations do not result in further loss of structural information. By providing a formal characterization, we propose a notion of translation correctness based on a simulation relation.