Containment of Conjunctive Queries over Databases with Null Values

Abstract

Abstract. We study containment of conjunctive queries that are evaluated over databases that may contain tuples with null values. We assume the semantics of SQL for single block queries with a SELECT DISTINCT clause. This problem ("null containment" for short) is different from containment over databases without null values and sometimes more difficult. We show that null-containment for boolean conjunctive queries is NPcomplete while it is Π P 2 -complete for queries with distinguished variables. However, if no relation symbol is allowed to appear more than twice, then null-containment is polynomial, as it is for databases without nulls. If we add a unary test predicate IS NULL, as it is available in SQL, then containment becomes Π P 2 -hard for boolean queries, while it remains in Π P 2 for arbitrary queries.

SVTe

“…The aim is to prune the search of possible counterexamples by generating only the relevant ones but, at the same time, without diminishing the requirement of completeness. Treatment of null values is performed according to the ideas developed in [8].…”

Parallel-Correctness and Containment for Conjunctive Queries with Union and Negation

“…As mentioned in the introduc-tion, the latter apparently only holds when the database schema is fixed or the arity of relations is considered to be bounded. A proof for the Π p 2 -lowerbound is given by Farré et al [12]. Based on [15], Wei and Lausen [19] study a method for testing containment that exploits containment mappings for the positive parts of queries, and additionally provide a characterisation for UCQ ¬ containment.…”

Improved Cardinality Estimation by Learning Queries Containment Rates

“…In [15] it was proved that for every k ≥ 1, conjunctive query containment could be solved in polynomial time, if Q2 has querywidth smaller than k +1. In addition to the mentioned cases, there are many other tractable cases [44,11,12,19]. Such cases are obtained by imposing syntactic or structural restrictions on the input queries Q1 and Q2.…”

“…equivalent to), query Q2, analytically, if for all the database states D, Q1's result over D is contained in (resp., equals) Q2's result over D. Query containment is a well-known concept that has applications in query optimization. It has been extensively researched in database theory, and many algorithms were proposed for determining containment under different assumptions [44,11,12,19]. However, determining query containment analytically is not practically sufficient.…”