Storage architectures ranging from minimum bandwidth regenerating encoded distributed storage systems to declustered-parity RAIDs can be designed using dense partial Steiner systems in order to support fast reads, writes, and recovery of failed storage units. In order to ensure good performance, popularities of the data items should be taken into account and the frequencies of accesses to the storage units made as uniform as possible. A proposed combinatorial model ranks items by popularity and assigns data items to elements in a dense partial Steiner system so that the sums of ranks of the elements in each block are as equal as possible. By developing necessary conditions in terms of independent sets, we demonstrate that certain Steiner systems must have a much larger difference between the largest and smallest block sums than is dictated by an elementary lower bound. In contrast, we also show that certain dense partial $S(t, t+1, v)$ designs can be labeled to realize the elementary lower bound. Furthermore, we prove that for every admissible order $v$, there is a Steiner triple system $(S(2, 3, v))$ whose largest difference in block sums is within an additive constant of the lower bound.

中文翻译：

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通过标记部分 Steiner 系统来平衡存储系统中的访问

从最小带宽再生编码分布式存储系统到分簇奇偶校验 RAID 的存储架构都可以使用密集的部分 Steiner 系统进行设计，以支持故障存储单元的快速读取、写入和恢复。为了确保良好的性能，应考虑数据项的流行性，并尽可能统一访问存储单元的频率。建议的组合模型按受欢迎程度对项目进行排名，并将数据项分配给密集部分 Steiner 系统中的元素，以便每个块中元素的排名总和尽可能相等。通过在独立集合方面开发必要条件，我们证明某些 Steiner 系统在最大和最小块和之间的差异必须比基本下界所规定的要大得多。相比之下，我们还表明可以标记某些密集的部分 $S(t, t+1, v)$ 设计以实现基本下界。此外，我们证明对于每个可接纳的订单 $v$，存在一个 Steiner 三元系统 $(S(2, 3, v))$，其块总和的最大差异在下界的加性常数内。