Complex event recognition meets hierarchical conjunctive queries

Abstract

Hierarchical conjunctive queries (HCQ) are a subclass of conjunctive queries (CQ) with robust algorithmic properties. Among others, Berkholz, Keppeler, and Schweikardt have shown that HCQ is the subclass of CQ (without projection) that admits dynamic query evaluation with constant update time and constant delay enumeration. On a different but related setting stands Complex Event Recognition (CER), a prominent technology for evaluating sequence patterns over streams. Since one can interpret a data stream as an unbounded sequence of inserts in dynamic query evaluation, it is natural to ask to which extent CER can take advantage of HCQ to find a robust class of queries that can be evaluated efficiently. In this paper, we search to combine HCQ with sequence patterns to find a class of CER queries that can get the best of both worlds. To reach this goal, we propose a class of complex event automata model called Parallelized Complex Event Automata (PCEA) for evaluating CER queries with correlation (i.e., joins) over streams. This model allows us to express sequence patterns and compare values among tuples, but it also allows us to express conjunctions by incorporating a novel form of non-determinism that we call parallelization. We show that for every HCQ (under bag semantics), we can construct an equivalent PCEA. Further, we show that HCQ is the biggest class of acyclic CQ that this automata model can define. Then, PCEA stands as a sweet spot that precisely expresses HCQ (i.e., among acyclic CQ) and extends them with sequence patterns. Finally, we show that PCEA also inherits the good algorithmic properties of HCQ by presenting a streaming evaluation algorithm under sliding windows with logarithmic update time and output-linear delay for the class of PCEA with equality predicates.