Algorithms for Computing Approximate Certain Answers over Incomplete Databases

Incomplete information arises in many database applications, such as data integration, data exchange, inconsistency management, data cleaning, ontological reasoning, and many others. A principled way of answering queries over incomplete databases is to compute certain answers, which are query answers that can be obtained from every complete database represented by an incomplete one. For databases containing (labeled) nulls, certain answers to positive queries can be easily computed in polynomial time, but for more general queries with negation the problem becomes coNP-hard. To make query answering feasible in practice, one might resort to SQL's evaluation, but unfortunately, the way SQL behaves in the presence of nulls may result in wrong answers. Thus, on the one hand, SQL's evaluation is efficient but flawed, on the other hand, certain answers are a principled semantics but with high complexity. To deal with issue, recent research has focused on developing polynomial time approximation algorithms for computing (approximate) certain answers. This paper surveys recent advances in this area.