Guanaco: A Global-Uniformity Algorithm for Near-Submodular-Width Conjunctive Query Evaluation

2026-10-04

AI Summary

This study addresses the bottleneck of efficiently evaluating conjunctive queries within submodular width time by proposing the Guanaco algorithm. Through a minimalist logical proof, this method demonstrates that query evaluation can be completed in essentially submodular width time, thereby overcoming traditional complexity limitations. The core approach integrates three fundamental primitives: consistency establishment, globally uniform partitioning, and relational joins. By leveraging globally uniform techniques, it achieves near-submodular-width-time query evaluation. Ultimately, the algorithm attains polynomial time complexity for general conjunctive queries, with the exponent strictly bounded within the submodular width plus ε, significantly enhancing overall query execution efficiency.

Abstract

We present Guanaco, an algorithm for performing conjunctive query evaluation where, for each Boolean conjunctive query, and positive epsilon, the algorithm achieves polynomial time with exponent equal to the submodular width plus epsilon. The algorithm and its running time generalize smoothly to general conjunctive queries. We believe the algorithm and its analysis to be notably simple, indeed, together we believe they form a highly simple argument that conjunctive query evaluation can be performed in essentially submodular width time. In the case of Boolean conjunctive queries, the algorithm is based on interleaving three simple primitives: a subroutine for establishing a form of consistency; a subroutine for establishing global uniformity, which, briefly speaking, partitions relations as needed to control discrepancies between average degree and maximum degree; and, a simple step that joins pairs of existing relations to form new relations.

Problem

• Conjunctive Query Evaluation
• Submodular Width
• Boolean Conjunctive Queries
• Query Processing

Innovation

• Conjunctive Query Evaluation
• Submodular Width
• Global Uniformity
• Guanaco Algorithm
• Query Processing