How can complex data relationships be simplified? This paper introduces a precise notion of independence for relations in multiattribute relations or multicolumn tables, drawing an analogy to factors in a Cartesian product or orthogonal components of a vector. The research defines and studies this notion of independence to decompose complex relationships. The central result demonstrates that the original relation can be reconstructed from its independent components using the natural join operation. The study also shows that independent components split the full family of functional dependencies into corresponding component families, offering a criterion for independence. This work provides a valuable framework for simplifying and understanding complex data relationships. By identifying independent components, it enables easier analysis and manipulation of data, with implications for database design and data management.
Published in _ACM Transactions on Database Systems_, this paper aligns with the journal's focus on database theory and systems. The research contributes to the journal's scope by introducing a new concept of independence for relations, providing tools for data decomposition, and improving database system analysis.