We reformulate the definition of privacy in the private information retrieval (PIR) problem to accommodate flexible privacy requirements. We focus on graph-replicated PIR, with a generalized privacy requirement, instead of requiring all messages to be private from all servers, during retrieval. Towards this, we define a privacy requirement set for each server, which can be an arbitrary subset of all message indices, as long as the stored message indices are in their privacy requirement set. Since both the storage and privacy requirement sets have many possibilities, we focus on two specific storage settings, namely the path and cyclic graphs. We consider several privacy settings for each of them, which are not necessarily the same, to give different examples for privacy sets. Of particular interest are the privacy sets that comprise the indices of messages stored at servers within a neighborhood range. The neighborhood range parameter allows a transition from the recently introduced local PIR [1] to the standard graph-replicated PIR. In these cases, we derive bounds on the capacity or find the exact capacity.

翻译：我们重新表述了私有信息检索（PIR）问题中隐私的定义，以适应灵活化的隐私需求。本文聚焦于图复制型PIR，采用广义隐私需求，即在检索过程中不再要求所有消息对所有服务器均保持私有。为此，我们为每台服务器定义了一个隐私需求集合，该集合可以是全部消息索引的任意子集，前提是存储的消息索引属于其隐私需求集合。由于存储集合与隐私需求集合存在多种可能，我们重点分析两种特定的存储结构，即路径图与循环图。针对每种结构，我们考虑若干互不相同的隐私设置，以提供隐私集合的不同实例。特别值得关注的是，由服务器邻域范围内存储的消息索引构成的隐私集合。邻域范围参数使得从近期提出的局部PIR[1]到标准图复制型PIR的转化成为可能。在相关情形下，我们推导出容量的下界或确定其精确值。