AI 中文总结
该研究针对加权图建模的地理分布式存储系统，证明k≥3时延迟最优文件分配是NP难的，确定了可实现该分配的网络拓扑并给出高效构造算法。
AI 中文摘要
我们研究以加权图建模的地理分布式存储系统中的延迟最优文件分配问题，其中边权重表示通信延迟，每个节点存储一个（可能经过编码的）文件。我们的目标是最小化均匀选取所有节点和文件时，检索原始文件所需的平均时间。我们证明，对于每个固定的文件数量k≥3，通过从支配数问题归约可知，计算延迟最小化的分配是NP难的。在积极方面，我们确定了可接受未编码结构化最优分配的自然网络拓扑，其中每个节点可选择k个最近节点（包含自身）来存储不同的原始文件。我们证明，每个加权树、某些加权环以及具有足够大最小度的单位权重图都可接受此类分配。对于这些图类，我们提供了构造延迟最优文件分配的高效算法。
英文摘要
We study latency-optimal file assignment in geo-distributed storage systems modeled as weighted graphs, where edge weights represent communication delays and each node stores one (possibly coded) file. Our goal is to minimize the average time required to retrieve an original file, taken uniformly over all nodes and files. We show that for every fixed number of files $k \geq 3$, computing a latency-minimizing assignment is NP-hard via a reduction from the domatic number problem. On the positive side, we identify natural network topologies that admit uncoded, structured optimal assignments in which, for every node, one can choose its $k$ closest nodes, including itself, so that they store distinct original files. We prove that every weighted tree, certain weighted cycles, and unit-weight graphs with sufficiently large minimum degree admit such assignments. For these graph classes, we provide efficient algorithms to construct latency-optimal file assignments.
CommentsAccepted to the 2026 IEEE Information Theory Workshop (ITW 2026)
