CIF: Small: Collaborative Research:Leveraging Data Popularity in Distributed Storage Systems via Constrained Design Theory

近年来，大规模分布式存储系统的实现以及伴随而来的数据分析和编码方法激增，使其能够可靠、安全和低延迟地运行。然而，在许多系统研究中，与系统访问控制、隐私信息检索和计算复杂性有很大关系的重要数据需求(流行度)特征在很大程度上被忽视了。这在一定程度上可以归因于这样一个事实，即大多数云存储设施对热数据和冷数据采用不同的存储平台，从而在一定程度上解决了与可变数据需求相关的问题。但即使在冷热数据类别中，数据的受欢迎程度也存在显著差异，这带来了许多不平凡的系统设计挑战。为了解决这些问题，拟议的研究计划旨在开发一类新的数学对象，称为约束设计，特别是Steiner系统。设计表示基本集合的子集的有限集合，其元素满足关于集合相交和排列的预定义对称约束。设计的元素与数据块相关联，而元素的子集表示要存储在同一磁盘或服务器上的数据块；鉴于其简单性和丰富的数学结构，设计已在许多实际的分布式存储系统平台中获得巨大成功。在对对象和数据文件的需求不统一的情况下，仅有交集约束不能确保潜在的实现约束。因此，元素必须配备非负的流行度值，并且底层的组合设计必须被修改以满足由数据流行度值实施的额外的代数和频率约束。这一新模型导致了一系列关于构造加权和标记组合设计的具有挑战性的数学问题的独特集合。要考虑的具体问题包括开发平衡服务器访问的设计、在存在流行边信息的情况下进行私人信息检索以及标签批次代码的横向设计。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Recent years have witnessed a surge of large-scale distributed storage system implementations and accompanying data analyses and coding methods that enable their reliable, secure and low-delay operation. Nevertheless, in many system studies, important data demand (popularity) features which have a strong bearing on system access control, private information retrieval and computational complexity have been largely overlooked. This can be attributed in part to the fact that most cloud storage facilities employ different storage platforms for hot and cold data, thereby partly addressing problems associated with variable data demands. But even within the hot and cold data categories there exist significant variations in data popularity that create many nontrivial system design challenges.To address these issues, the proposed research program aims to develop a new family of mathematical objects termed constrained designs and Steiner systems in particular. Designs represent finite collections of subsets of a ground set whose elements satisfy predefined symmetry constraints with respect to set intersections and arrangements. Elements of a design are associated with data chunks, while subsets of elements represent data chunks to be stored on the same disk or server; given their simplicity and rich mathematical structure, designs have been used with great success in many practical distributed storage system platforms. In the presence of nonuniform demands for objects and data files, intersection constraints alone fail to ensure underlying implementation constraints. Consequently, elements have to be equipped with nonnegative popularity values, and the underlying combinatorial designs modified to satisfy additional algebraic and frequency constraints enforced by data popularity values. This new model leads to a unique collection of challenging mathematical problems regarding constructions of weighted and labeled combinatorial designs. Particular problems to be considered include developing designs for balanced server access, private information retrieval in the presence of popularity side information and transversal designs for labeled batch codes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.