AI 中文总结
本研究完全解决了一元函数依赖场景下的最优更新修复问题，证明该场景下的最优更新修复要么属于已知易处理类，要么为NP难问题，推进了函数依赖最优修复问题的研究进展。
AI 中文摘要
如果一个表违反了其所需的函数依赖（FDs）集合，那么恢复一致性所需的最小单元格修改次数是多少？这个被称为寻找最优更新修复（U-repair）的基础问题，目前仅在少数特定FD集合下存在多项式时间算法。是否存在额外的易处理情形仍是一个开放问题。该问题唯一已确立的难解性结果来自Kolahi和Lakshmanan（2009）；后续尝试证明其他情形的难解性均未成功，使得这些情形仍未解决。本研究在该开放问题上取得了重大进展，完全解决了一元FDs的情形，其中每个FD的左侧仅有一个属性。研究表明，每一组一元FDs要么属于先前已知的易处理类别，要么使得寻找最优U-repair的问题成为NP难问题。
英文摘要
If a table violates its required set of functional dependencies (FDs), what is the minimum number of cell changes needed to restore consistency? This fundamental problem, known as finding an optimal update repair (U-repair), is known to admit polynomial-time algorithms only for a small number of specific FD sets. Whether additional tractable cases exist has remained open. The only established hardness result for this problem is due to Kolahi and Lakshmanan (2009); subsequent attempts to prove hardness for additional cases have failed, leaving these cases unresolved. In this work, we make substantial progress on this open problem by completely resolving the case of unary FDs, in which every FD has a single attribute on its left-hand side. We show that every set of unary FDs either falls into one of the previously known tractable classes or makes the problem of finding an optimal U-repair NP-hard.
