The Dynamic Yannakakis Algorithm

Abstract

Modern computing tasks such as real-time analytics require refresh of query results under high update rates. Incremental View Maintenance (IVM) approaches this problem by materializing results in order to avoid recomputation. IVM naturally induces a trade-off between the space needed to maintain the materialized results and the time used to process updates. In this paper, we show that the full materialization of results is a barrier for more general optimization strategies. In particular, we present a new approach for evaluating queries under updates. Instead of the materialization of results, we require a data structure that allows: (1) linear time maintenance under updates, (2) constant-delay enumeration of the output, (3) constant-time lookups in the output, while (4) using only linear space in the size of the database. We call such a structure a Dynamic Constant-delay Linear Representation (DCLR) for the query. We show that DYN, a dynamic version of the Yannakakis algorithm, yields DCLRs for the class of free-connex acyclic CQs. We show that this is optimal in the sense that no DCLR can exist for CQs that are not free-connex acyclic. Moreover, we identify a sub-class of queries for which DYN features constant-time update per tuple and show that this class is maximal. Finally, using the TPC-H and TPC-DS benchmarks, we experimentally compare DYN and a higher-order IVM (HIVM) engine. Our approach is not only more efficient in terms of memory consumption (as expected), but is also consistently faster in processing updates.