Maintenance of datalog materialisations revisited.

Datalog is a rule-based formalism that can axiomatise recursive properties such as reachability and transitive closure. Datalog implementations often materialise (i.e., precompute and store) all facts entailed by a datalog program and a set of explicit facts. Queries can thus be answered directly in the materialised facts, which is beneficial to the performance of query answering, but the materialised facts must be updated whenever the explicit facts change. Rematerialising all facts ‘from scratch’ can be very inefficient, so numerous materialisation maintenance algorithms have been developed that aim to efficiently identify the facts that require updating and thus reduce the overall work. Most such approaches are variants of the counting or Delete/Rederive (DRed) algorithms. Algorithms in the former group maintain additional data structures and are usually applicable only if datalog rules are not recursive, which limits their applicability in practice. Algorithms in the latter group do not require additional data structures and can handle recursive rules, but they can be inefficient when facts have multiple derivations. Finally, to the best of our knowledge, these approaches have not been compared and their practical applicability has not been investigated. Datalog is becoming increasingly important in practice, so a more comprehensive understanding of the tradeoffs between different approaches to materialisation maintenance is needed. In this paper we present three such algorithms for datalog with stratified negation: a new counting algorithm that can handle recursive rules, an optimised variant of the DRed algorithm that does not repeat derivations, and a new Forward/Backward/Forward (FBF) algorithm that extends DRed to better handle facts with multiple derivations. Furthermore, we study the worst-case performance of these algorithms and compare the algorithms' behaviour on several examples. Finally, we present the results of an extensive, first-of-a-kind empirical evaluation in which we investigate the robustness and the scaling behaviour of our algorithms. We thus provide important theoretical and practical insights into all three algorithms that will provide invaluable guidance to future implementors of datalog systems.