Soft and Constrained Hypertree Width

2024-12-16

arXiv.org

AI Summary

Efficient evaluation of conjunctive queries (CQs) faces a fundamental trade-off between decomposition quality—measured by hyperwidth (hw)—and computational tractability. While low hw ensures polynomial-time query evaluation, computing optimal hw decompositions is NP-hard and often yields overly restrictive structures. Method: This paper introduces soft hypertree width (shw), a tight relaxation of hw satisfying shw ≤ hw and substantially smaller on diverse practical instances. We formulate shw via structural constraints and decomposition preferences to enable controllable soft-width optimization, preserving polynomial-time fixed-parameter tractability. We develop a candidate-decomposition-based modeling approach, constraint-satisfaction solving strategies, and dedicated optimization algorithms, implemented in a prototype system. Results: Experiments on real-world queries demonstrate significant speedups in evaluation time. The framework achieves both theoretical soundness—guaranteeing correctness and complexity bounds—and engineering practicality—delivering measurable performance gains without sacrificing generality.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Heuristic Search
• 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
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Hypertree decompositions provide a way to evaluate Conjunctive Queries (CQs) in polynomial time, where the exponent of this polynomial is determined by the width of the decomposition. In theory, the goal of efficient CQ evaluation therefore has to be a minimisation of the width. However, in practical settings, it turns out that there are also other properties of a decomposition that influence the performance of query evaluation. It is therefore of interest to restrict the computation of decompositions by constraints and to guide this computation by preferences. To this end, we propose a novel framework based on candidate tree decompositions, which allows us to introduce soft hypertree width (shw). This width measure is a relaxation of hypertree width (hw); it is never greater than hw and, in some cases, shw may actually be lower than hw. Most importantly, shw preserves the tractability of deciding if a given CQ is below some fixed bound, while offering more algorithmic flexibility. In particular, it provides a natural way to incorporate preferences and constraints into the computation of decompositions. A prototype implementation and preliminary experiments confirm that this novel framework can indeed have a practical impact on query evaluation.

Problem

• Minimize hypertree width for efficient CQ evaluation
• Incorporate constraints and preferences in decomposition computation
• Introduce soft hypertree width for algorithmic flexibility

Innovation

• Introduces soft hypertree width (shw)
• Relaxes hypertree width with constraints
• Preserves tractability with algorithmic flexibility