This article studies discovery of Graph Functional Dependencies (GFDs), a class of functional dependencies defined on graphs. We investigate the fixed-parameter tractability of three fundamental problems related to GFD discovery. We show that the implication and satisfiability problems are fixed-parameter tractable, but the validation problem is co-W[1]-hard in general. We introduce notions of reduced GFDs and their topological support, and formalize the discovery problem for GFDs. We develop algorithms for discovering GFDs and computing their covers. Moreover, we show that GFD discovery is feasible over large-scale graphs, by providing parallel scalable algorithms that guarantee to reduce running time when more processors are used. Using real-life and synthetic data, we experimentally verify the effectiveness and scalability of the algorithms.

中文翻译：

---

发现图函数依赖

本文研究图函数依赖 (GFD) 的发现，这是在图上定义的一类函数依赖。我们研究了与 GFD 发现相关的三个基本问题的固定参数可处理性。我们证明了隐含和可满足性问题是固定参数可处理的，但验证问题通常是 co-W[1]-hard。我们介绍了减少 GFD 的概念及其拓扑支持，并将 GFD 的发现问题形式化。我们开发用于发现 GFD 并计算其覆盖率的算法。此外，我们通过提供可保证在使用更多处理器时减少运行时间的并行可扩展算法，证明 GFD 发现在大规模图上是可行的。使用现实生活和合成数据，我们通过实验验证了算法的有效性和可扩展性。