🤖 AI Summary
This paper investigates conditional lower bounds for the evaluation complexity of conjunctive queries (CQs) under Boolean testing, counting, enumeration, and direct-access computation models. To address fundamental performance bottlenecks resistant to existing algorithms, the authors employ fine-grained complexity assumptions—including 3SUM and APSP—and integrate parameterized analysis with conditional lower-bound proof techniques. They establish the first tight conditional lower bounds for multiple CQ variants, demonstrating that, under standard hypotheses, current state-of-the-art algorithms are asymptotically optimal—any further improvement faces inherent barriers. The work systematically characterizes the complexity landscape across diverse query semantics and computational models, thereby providing rigorous theoretical limits for query optimization. These results significantly advance the understanding of the intrinsic feasibility and hardness of relational query processing.
📝 Abstract
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus will be on showing how different relatively recent hypotheses from complexity theory connect to query answering and allow showing that known algorithms in several cases can likely not be improved.