Functional dependencies (FDs) are basic constraints in relational databases and are used for many data management tasks. Most FD discovery algorithms find all valid dependencies, but this causes two problems. First, the computational cost is prohibitive: computational complexity grows quadratically with the number of tuples and exponentially with the number of attributes, making discovery slow on large-scale and high-dimensional data. Second, the result set can be huge, making it hard to identify useful dependencies. We propose SDP (Selective-Discovery-and-Prune), which discovers the top-$k$ FDs ranked by redundancy count. Redundancy count measures how much duplicated information an FD explains and connects directly to storage overhead and update anomalies. SDP uses an upper bound on redundancy to prune the search space. It is proved that this upper bound is monotone: adding attributes refines partitions and thus decreases the bound. Once the bound falls below the top-$k$ threshold, the entire branch can be skipped. We improve SDP with three optimizations: ordering attributes by partition cardinality, using pairwise statistics in a Partition Cardinality Matrix to tighten bounds, and a global scheduler to explore promising branches first. Experiments on over 40 datasets show that SDP is much faster and uses less memory than exhaustive methods.

翻译：函数依赖是关系数据库中的基本约束，被用于许多数据管理任务。大多数函数依赖发现算法会找出所有有效的依赖，但这会导致两个问题。首先，计算成本过高：计算复杂度随元组数量呈二次增长，随属性数量呈指数增长，使得在大规模和高维数据上的发现过程缓慢。其次，结果集可能非常庞大，难以识别出有用的依赖。我们提出了SDP（选择性发现与剪枝）算法，该算法发现按冗余计数排序的Top-$k$函数依赖。冗余计数衡量了一个函数依赖所解释的重复信息量，并直接关联到存储开销和更新异常。SDP利用冗余的上界来剪枝搜索空间。我们证明了该上界是单调的：增加属性会细化划分，从而降低该上界。一旦该上界低于Top-$k$阈值，整个分支即可被跳过。我们通过三项优化改进了SDP：按划分基数对属性排序、在划分基数矩阵中使用成对统计以收紧上界，以及使用全局调度器优先探索有希望的分支。在超过40个数据集上的实验表明，SDP比穷举方法快得多，且内存使用更少。