The Complexity of Finding Missing Answer Repairs

TL;DR

This paper explores the computational complexity of identifying database repairs for missing query answers, revealing polynomial-time solvable subclasses and NP-hard cases, with implications for query types and recursion.

Contribution

It characterizes the complexity landscape of the minimal repair problem for various query classes, including unions of conjunctive queries with negation and semi-positive datalog.

Findings

Polynomial-time solutions for certain query subclasses.

NP-hardness and inapproximability results for others.

Data complexity allows polynomial-time repair identification for semi-positive datalog queries.

Abstract

We investigate the problem of identifying database repairs for missing tuples in query answers. We show that when the query is part of the input - the combined complexity setting - determining whether or not a repair exists is polynomial-time is equivalent to the satisfiability problem for classes of queries admitting a weak form of projection and selection. We then identify the sub-classes of unions of conjunctive queries with negated atoms, defined by the relational algebra operations permitted to appear in the query, for which the minimal repair problem can be solved in polynomial time. In contrast, we show that the problem is NP-hard, as well as set cover-hard to approximate via strict reductions, whenever both projection and join are permitted in the input query. Additionally, we show that finding the size of a minimal repair for unions of conjunctive queries (with negated atoms permitted) is OptP[log(n)]-complete, while computing a minimal repair is possible with O($n^2$) queries to an NP oracle. With recursion permitted, the combined complexity of all of these variants increases significantly, with an EXP lower bound. However, from the data complexity perspective, we show that minimal repairs can be identified in polynomial time for all queries expressible as semi-positive datalog programs.