Relational Conditional Set Operations

• Ano de defesa: 2021
• Autor(a) principal: Lescano, Alexis Iván Aspauza
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Álgebra relacional; Operações de conjuntos; Relational Algebra; Set Operations; Teoria de conjuntos; Theory of Sets
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-21012022-152207/

A set is a collection of different objects. Some basic operations from the Theory of Sets are the set membership (), subset (), intersection (), and difference (). The relational Algebra adapts the set operations to work with relations. However, as we show in this work, the set operations have limitations because of the implicit use of the identity predicate. That is, a tuple is a member of a set if it is identical to any tuple in the set. For example, lets consider two relations. The first one is a list of products that a person wants to buy. The second one is a list of products that one store has. Now, we could get any item from the desired products list and query can we buy this item in the store? with the set membership operator (), being true if the item is a member of the second set or false if not. With the set membership operator as a basis, we can also perform other queries such as subset, intersection, and difference. The subset () query would answer to can I buy all the desired products in the store?. The intersection () would answer to what products can I buy in the store? And finally, the difference () would answer to what are the desired products that I cannot buy in the store?. Still, many applications need other comparison predicates that are not limited to identity. For example, if we add quantity and price to the sets of desired products and stores products, comparing the tuples by identity wont have much sense, since a product in the store with stock greater than the required should be valid, and it is also valid a product with a price lower than the users maximum budget for that product. This MSc work presents the new Relational Conditional Set Operations. The novel operators encapsulate the idea of set operations with conditional queries, facilitating specific operators for them, and allowing their optimization. For example, they are potentially useful in applications of product sales with units and prices, job promotions with skills that have enough experience or certification level, and internships with minimum grades. We validate our proposals semantics and scalability by studying the first of these applications. Also, we open path for future works such as: to implement the operators in a DBMS; to propose SQL queries able to answer these kind of queries and compare it with our current approach; to extend the idea for bag algebra; to explore a whole new path of optimization for our algorithms; to add support for complex data, allowing similarity comparisons in the predicate; and, to study the use of these operators as basis for other operations that currently use the traditional set operation as basis; among others.