The resilience of conjunctive queries with inequalities

Abstract

The resilience of a query q (RES(q)) measures the minimum number of source tuples responsible for a specific query answer. If q is an IQ query, whose at most one attribute from a table has inequality relationships with attributions from other tables, the state-of-the-art work had shown that RES(q) is in PTIME. However, the state-of-the-art work is inefficient for computing the resilience of IQ queries. Moreover, the complexity of resilience for self-join free (sj-free) CQs with other kinds of inequalities has not been explored. Therefore, we provide a dichotomy for the complexity of resilience for sj-free CQs with inequalities q in this paper. We first introduce query condition graph, which includes a special query condition graph called query condition triad, and triangle vertex cover problem. Then we reduce the vertex cover problem to the triangle vertex cover problem. According to query condition graphs, our dichotomy is as follows: If q is a qc-triad query, which is not an IQ query but contains a query condition triad, then RES(q) is NP-complete. If q is a qc-linear query, which neither is an IQ query nor contains a query condition triad, then RES(q) is in PTIME. Finally, we introduce an algorithm called Rlin to compute the resilience of qc-linear queries, and an efficient algorithm named RIQ to efficiently compute the resilience of IQ queries. The experiments show that our RIQ has much better performance than other algorithms for computing the resilience of IQ queries.