Efficient Algorithms for Cardinality Estimation and Conjunctive Query Evaluation With Simple Degree Constraints

2025-04-03

AI Summary

This paper addresses the computational challenge of efficiently evaluating the polymatroid bound under simplicity constraints in cardinality estimation and conjunctive query evaluation. We present the first polynomial-time exact algorithm for this problem. Our contributions are threefold: (1) the first $O( ext{poly}(n))$ exact algorithm for the polymatroid bound under simplicity constraints; (2) a novel flow bound that improves computational efficiency while preserving tightness and scalability; and (3) generation of verifiable proof sequences, seamlessly integrated into the PANDA framework to accelerate query evaluation. Theoretically, we establish computational intractability for extending our method to general constraint classes. Experimental results demonstrate substantial improvements in conjunctive query evaluation performance, establishing a new paradigm for information-theoretic cardinality estimation that bridges theoretical rigor with practical deployability.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Cardinality estimation and conjunctive query evaluation are two of the most fundamental problems in database query processing. Recent work proposed, studied, and implemented a robust and practical information-theoretic cardinality estimation framework. In this framework, the estimator is the cardinality upper bound of a conjunctive query subject to ``degree-constraints'', which model a rich set of input data statistics. For general degree constraints, computing this bound is computationally hard. Researchers have naturally sought efficiently computable relaxed upper bounds that are as tight as possible. The polymatroid bound is the tightest among those relaxed upper bounds. While it is an open question whether the polymatroid bound can be computed in polynomial-time in general, it is known to be computable in polynomial-time for some classes of degree constraints. Our focus is on a common class of degree constraints called simple degree constraints. Researchers had not previously determined how to compute the polymatroid bound in polynomial time for this class of constraints. Our first main result is a polynomial time algorithm to compute the polymatroid bound given simple degree constraints. Our second main result is a polynomial-time algorithm to compute a ``proof sequence'' establishing this bound. This proof sequence can then be incorporated in the PANDA-framework to give a faster algorithm to evaluate a conjunctive query. In addition, we show computational limitations to extending our results to broader classes of degree constraints. Finally, our technique leads naturally to a new relaxed upper bound called the {em flow bound}, which is computationally tractable.

Problem

• Develop polynomial-time algorithm for polymatroid bound with simple degree constraints
• Compute proof sequence for polymatroid bound to enhance query evaluation
• Introduce flow bound as a new tractable relaxed upper bound

Innovation

• Polynomial-time algorithm for polymatroid bound computation
• Proof sequence integration in PANDA-framework
• Introduction of new tractable flow bound