Numbering Combinations for Compact Representation of Many-to-Many Relationship Sets

TL;DR

This paper introduces a novel encoding method for many-to-many relationship sets using combinatorial number systems, enabling compact representation within a single column in relational databases.

Contribution

It presents a new combinatorial encoding approach for many-to-many relationships that simplifies database design and improves efficiency by avoiding separate relationship tables.

Findings

Encoding reduces storage by consolidating relationships into one column.

The method enables unique identification of entity combinations.

Introduces Rank-Join operation for relational algebra integration.

Abstract

In this paper we propose an approach to implement specific relation-ship set between two entities called combinatorial relationship set. For the combinatorial relationship set B between entity sets G and I the mapping cardinality is many-to-many. Additionally, entities from G can be uniquely encoded with a pair of values (h, k) generated with the procedure for numbering combinations of entities from I. The encoding procedure is based on combinatorial number system that provides a representation of all possible k -combinations of a set of n elements by a single number. In general many-to-many relationship sets are represented by a relation or table, while the combinatorial relationship is not physically stored as separate table. However, all information is encapsulated into a single column added to G. The new column is a candidate key in G. Additional operation named Rank-Join to fundamental relational-algebra is presented to combine information from g and i associated with a combinatorial relationship set. Motivation for combinatorial relationship originates from challenges in designing and implementing multivalued dimensions and bridge tables in data-warehouse models.