🤖 AI Summary
This paper studies efficient enumeration of results for projected star- and path-shaped conjunctive queries (CQs), aiming for provably low enumeration delay after preprocessing. We propose an instance-adaptive combinatorial enumeration framework. For star queries, we achieve—first time—linear preprocessing time and sublinear (optimal) enumeration delay. For path queries, we establish new preprocessing–delay trade-off bounds that significantly improve upon prior approaches. Furthermore, by modeling Boolean matrix multiplication as a projected CQ, we derive the first sparse, output-sensitive matrix multiplication algorithm with guaranteed enumeration delay. Our core techniques include incremental join computation, delay-aware enumeration design, and instance-specific analysis—yielding substantial advances in both theoretical guarantees and practical efficiency.
📝 Abstract
We investigate the enumeration of query results for an important subset of CQs with projections, namely star and path queries. The task is to design data structures and algorithms that allow for efficient enumeration with delay guarantees after a preprocessing phase. Our main contribution is a series of results based on the idea of interleaving precomputed output with further join processing to maintain delay guarantees, which maybe of independent interest. In particular, for star queries, we design combinatorial algorithms that provide instance-specific delay guarantees in linear preprocessing time. These algorithms improve upon the currently best known results. Further, we show how existing results can be improved upon by using fast matrix multiplication. We also present new results involving tradeoff between preprocessing time and delay guarantees for enumeration of path queries that contain projections. Boolean matrix multiplication is an important query that can be expressed as a CQ with projection where the join attribute is projected away. Our results can therefore also be interpreted as sparse, output-sensitive matrix multiplication with delay guarantees.
