Grammar-Constrained (CFL) Reachability: Subcubic Preprocessing, Indexing Trade-offs, and Structured Decoding Semantics

TL;DR

This paper introduces a new framework for efficiently evaluating context-free grammar-constrained reachability queries in graphs, analyzing theoretical bounds and empirically comparing algorithmic variants on real-world data.

Contribution

It provides a novel algorithmic framework with theoretical analysis and extensive empirical evaluation, revealing trade-offs and practical guidance for grammar-constrained reachability.

Findings

Grammar structure significantly affects performance.

Empirical results show trade-offs between different algorithms.

Guidelines for selecting efficient approaches in practice.

Abstract

We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free grammars, and analyze its theoretical runtime bounds. To complement our theoretical results, we conduct an extensive empirical evaluation on a comprehensive benchmark of real-world schemas, comparing different algorithmic variants and reporting performance trade-offs. Our results highlight the impact of grammar structure and graph characteristics on reachability computation, and provide guidance for selecting efficient approaches in practice.