I‑AIMS Institute for Artificial Intelligence
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Categorical Hypergraph Models for Distributed Data Fabrics

Tanush Shaska, Ilias Kotsireas

I-AIMS paper sh-99 · Published in Decision-Making, Optimization, and Data Analysis: Theory and Applications, Springer Optimization and Its Applications · 2026

The rapid proliferation of data from cloud computing, the Internet of Things (IoT), artificial intelligence (AI), and distributed systems has overwhelmed traditional data management frameworks. Centralized architectures, reliant on rigid schemas, struggle to integrate heterogeneous datasets, scale across distributed nodes, enforce governance, or support real-time analytics. Data fabrics address these issues by providing a unified, metadata-driven architecture for seamless integration, navigation, and analytics. We propose a mathematical framework for data fabrics, unifying heterogeneous data management in distributed systems through a hypergraph-based structure ℱ = (D, M, G, T, P, A). Datasets, metadata, transformations, policies, and analytics are modeled over a distributed system Σ = (N, C), with multi-way relationships encoded in a hypergraph G = (V, E). A categorical approach, with datasets as objects and transformations as morphisms, supports operations like data integration and federated learning. The hypergraph is embedded into a modular tensor category, capturing relational symmetries via braided monoidal structures, with geometric analogies to Hurwitz spaces enriching the algebraic modeling. We prove the NP-hardness of critical tasks, such as schema matching and dynamic partitioning, and propose spectral methods and symmetry-based alignments for scalable solutions. The framework ensures consistency, completeness, and causality under CAP and CAL theorems, leveraging sparse incidence matrices and braiding actions for fault-tolerant operations. Applied to a multicomponent architecture integrating databases, real-time analytics, and transformation pipelines, it supports efficient vector representations and demonstrates real-world viability through an Amazon seller scenario. This work advances theoretical foundations while providing practical tools for large-scale data ecosystems.

MSC classes: Primary 68P15; Secondary 18M15, 05C65

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