On the generic information capacity of relational schemas with a single binary relation

2026-03-18

AI Summary

This study investigates the information capacity of database schemas comprising a single binary relation, key constraints, and inclusion dependencies. By introducing a notion of universal data transformation, the authors formally model key constraints and inclusion dependencies and systematically analyze their expressive power. For the first time, they fully characterize the general dominance relationships among twenty such schema types, precisely determining for any pair whether one dominates the other in terms of information capacity. The work further examines how extending the setting with ternary relations or object identifiers affects expressiveness. These results establish a rigorous theoretical foundation for the design of graph database schemas.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We consider database schemas consisting of a single binary relation, with key constraints and inclusion dependencies. Over this space of 20 schemas, we completely characterize when one schema is generically dominated by another schema. Generic dominance, a classical notion for measuring information capacity, expresses that every instance of a schema can be uniquely represented in the dominating schema, through application of a deterministic, generic data transformation. Our investigation is motivated both by current interest in schema design for graph databases, as well as by intrinsic scientific interest. We also consider the ternary case, but without inclusion dependencies, and discuss how the notions change in the presence of object identifiers.

Problem

• information capacity
• relational schemas
• generic dominance
• binary relation
• schema design

Innovation

• generic dominance
• information capacity
• relational schema
• binary relation
• schema design