Conceitos Básicos
The core message of this article is to provide a complete complexity classification for the problem of counting database repairs, both exactly and approximately, in the presence of functional dependencies and conjunctive queries.
Resumo
The article discusses the problem of counting database repairs, which is crucial in the context of querying inconsistent databases. The key elements are:
- The notion of database repair, which is a consistent database that minimally deviates from the original inconsistent database.
- The problem of counting the number of repairs (♯Repairs(Σ)) and the number of repairs that entail a given query (♯Repairs(Σ, Q)).
The authors aim to provide a complete complexity classification for these counting problems, determining whether they are tractable (in FP) or intractable (♯P-complete).
For the exact counting problem:
- They lift the previous dichotomy result for primary keys and self-join-free conjunctive queries (SJFCQs) to the more general case of functional dependencies (FDs).
- They show that the dichotomy holds by exploiting the class of FDs with a left-hand side (LHS) chain.
For the approximate counting problem:
- They show that the existence of a fully polynomial-time randomized approximation scheme (FPRAS) is not guaranteed for FDs, in contrast to the case of primary keys.
- However, they prove that FDs with an LHS chain form an island of approximability, where an FPRAS exists.
These results provide crucial steps towards a complete classification of approximate counting of repairs in the case of FDs.
Estatísticas
The database in Figure 1 contains facts about a railroad company's schedule and station locations.
Citações
"Database integrity constraints allow us to specify semantic properties that should be satisfied by all databases of a certain relational schema."
"Real-life databases are often inconsistent, i.e., do not conform to their specifications in the form of integrity constraints."
"The key elements underlying the CQA approach are the notion of (database) repair and the notion of query answering based on certain answers."