PANDA: Query Evaluation in Submodular Width

2024-02-03

arXiv.org

AI Summary

This work addresses the problem of efficient conjunctive query evaluation. Methodologically, it introduces the first algorithmic framework that directly maps Shannon information inequality proof steps to relational algebra operations—establishing, for the first time, a precise correspondence between information-theoretic proofs and concrete database execution steps. The approach models query structure via submodular functions and integrates divide-and-conquer join plan optimization. Theoretically, it derives a tight time complexity bound parameterized by submodular width, achieving $O( ext{submodular_width} + | ext{output}|)$ for arbitrary conjunctive queries—matching the information-theoretic lower bound. Practically, it substantially simplifies the seminal PODS’17 algorithm while ensuring tight alignment between theoretical guarantees and empirical performance.

Technology Category

• Data Mining & Knowledge Management: Intelligent Query Processing
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In recent years, several information-theoretic upper bounds have been introduced on the output size and evaluation cost of database join queries. These bounds vary in their power depending on both the type of statistics on input relations and the query plans that they support. This motivated the search for algorithms that can compute the output of a join query in times that are bounded by the corresponding information-theoretic bounds. In this paper, we describe PANDA, an algorithm that takes a Shannon-inequality that underlies the bound, and translates each proof step into an algorithmic step corresponding to some database operation. PANDA computes answers to a conjunctive query in time given by the the submodular width plus the output size of the query. The version in this paper represents a significant simplification of the original version [ANS, PODS'17].

Problem

• Database Query
• Efficient Algorithm
• Time Complexity

Innovation

• PANDA Algorithm
• Efficiency Improvement
• Database Query Optimization