Numbering Combinations for Compact Representation of Many-to-Many Relationship Sets
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912686700232704 |
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| author | Tomovic, Savo |
| author_facet | Tomovic, Savo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numbering Combinations for Compact Representation of Many-to-Many Relationship Sets Tomovic, Savo Databases Discrete Mathematics 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. |
| title | Numbering Combinations for Compact Representation of Many-to-Many Relationship Sets |
| topic | Databases Discrete Mathematics |
| url | https://arxiv.org/abs/2511.02096 |