A theoretical and experimental comparison of algorithms for the containment of conjunctive queries with negation

Abstract

We tackle the containment problem for conjunctive queries with negation, which takes two queries q 1 and q 2 as input and asks if q 1 is contained in q 2. A general approach for solving this problem consists of considering all completions of q 1 (intuitively these completions represent all canonical databases that satisfy q 1) and checking if each completion yields the same answer on q 2. Since the total number of completions of q 1 is exponential in the size of q 1, several proposals have aimed at reducing the number (and the size) of the completions checked. In this paper, we propose a unifying framework for comparing algorithms following this general approach and define two kinds of heuristics for exploring the space of completions. Combining these heuristics with both classical kinds of traversals, i.e., depth-first and breadth-first, we obtain four algorithms that we compare experimentally with respect to running time on difficult instances of the containment problem. © 2011 Springer-Verlag Berlin Heidelberg.