Trade-offs in Static and Dynamic Evaluation of Hierarchical Queries

Abstract

We investigate trade-offs in static and dynamic evaluation of hierarchical queries with arbitrary free variables. In the static setting, the trade-off is between the time to partially compute the query result and the delay needed to enumerate its tuples. In the dynamic setting, we additionally consider the time needed to update the query result in the presence of single-tuple inserts and deletes to the input database. Our approach observes the degree of values in the database and uses different computation and maintenance strategies for high-degree and low-degree values. For the latter it partially computes the result, while for the former it computes enough information to allow for on-the-fly enumeration. The main result of this work defines the preprocessing time, the update time, and the enumeration delay as functions of the light/heavy threshold and of the factorization width of the hierarchical query. By conveniently choosing this threshold, our approach can recover a number of prior results when restricted to hierarchical queries. For a restricted class of hierarchical queries, our approach can achieve worst-case optimal update time and enumeration delay conditioned on the Online Matrix-Vector Multiplication Conjecture.