AF: Small: Scalable Algorithms for Data and Network Analysis

涉及大输入数据集的基于数据的决策需要大量时间让算法来处理它们。在计算机科学中，有效算法通常被认为是当输入大小增加时运行时间不会增加“太快”的算法。“可伸缩算法”是最有效的算法之一，因为它们的运行时间需要与问题大小接近线性甚至是次线性。换句话说，它们的复杂性随着输入大小的增加而优雅地缩放。在大数据时代，高效算法的需求比以往任何时候都要高。虽然大数据将我们带入了计算机科学先驱所设想的渐近世界，但问题规模的爆炸性增长也极大地挑战了经典的高效算法概念：根据传统的多项式时间特征，过去被认为是高效的算法可能不再足以解决当今的问题。高效的算法应该是可扩展的，这不仅是可取的，而且是必要的。因此，可扩展性，而不是多项式时间的可计算性，应该被提升为表征高效计算的中心复杂性概念，这将是网络科学和大数据算法设计的重点。该项目将重点关注可扩展算法的设计和分析。 其主要目标之一是在算法设计领域与网络科学和机器学习领域之间建立桥梁。 如果成功，该项目将有助于为设计新的可扩展数据和网络分析算法提供严格的算法框架。 通过关注算法效率的概念-如可扩展性-尊重这些学科的研究人员对大数据时代实用算法的敏感性，该项目旨在增加理论分析对这些领域研究人员的价值。 由于该项目将来自许多学科的想法结合在一个连贯的研究工作中，因此就该项目的成果所提供的讲座和教程将有助于其范围内的学科交叉。 理论算法的开发可能具有实际适用性，应该简化理论计算机科学之外的学生的算法教育，并允许在计算机科学教育的早期阶段讨论实际重要的算法。这项研究的跨学科性质将使博士生和网络科学，机器学习，数值分析和社会科学的研究人员更广泛地参与，因此将提高成功支持和与妇女和少数民族研究人员合作的机会。和组合技术，从拉普拉斯线性求解器和最大流/最小割的最新突破，到网络分析，数据挖掘和机器学习中出现的各种问题。 该项目旨在表明这些技术--包括高级采样，稀疏化和网络的局部探索--将在提高算法可扩展性方面发挥越来越大的作用。 它包含了几个开放的问题，从网络分析到分布抽样，再到实现这一目标的社会影响。 该项目还旨在通过提供新的算法来深入了解图上的各种动态过程，从而提高对静态图结构之外的网络方面的理解，以便为网络科学开发更好的算法理论。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Data-based decision-making involving big input data sets require a lot of time for algorithms to process them. In computer science, efficient algorithms are generally considered to be the ones whose running time does not increase "too fast" when input size grows. "Scalable algorithms" are among the most efficient algorithms, because their running time is required to be nearly linear or even sub-linear with respect to the problem size. In other words, their complexity scales gracefully when the input size scales up. In the age of Big Data, efficient algorithms are in higher demand now more than ever before. While big data takes us into the asymptotic world envisioned by the pioneers of computer science, the explosive growth of problem size has also significantly challenged the classical notion of efficient algorithms: Algorithms that used to be considered efficient, according to the traditional polynomial-time characterization, may no longer be adequate for solving today's problems. It is not just desirable, but essential, that efficient algorithms should be scalable. Thus, scalability, instead of polynomial-time computability, should be elevated to the central complexity notion for characterizing efficient computation, and this will be the focus of algorithm design for network sciences and big data. This project will focus on the design and analysis of scalable algorithms. One of its primary objective is to build bridges between the area of algorithm design and the fields of network sciences and machine learning. If successful, the project will help to provide a rigorous algorithmic framework for designing new scalable data and network analysis algorithms. By focusing on notions of algorithmic efficiency --- such as scalability --- that respect the sensibilities of researchers in these disciplines as to what constitutes a practical algorithm in the age of big data, this project aims to increase the value of theoretical analyses to researchers in these fields. As this project combines ideas from many disciplines within one coherent research effort, lectures and tutorials presented on the fruits of the project will help cross-fertilize the disciplines within its scope. The development of theoretical algorithms that might have practical applicability should simplify education in algorithms for students beyond theoretical computer science, and allow discussion of practically important heuristics at early stages of computer science education. The interdisciplinary nature of this research will enable broader engagements with PhD students and researchers in network sciences, machine learning, numerical analysis, and social science and hence will enhance the chance to be successful in supporting and working with women and minority researchers.The technical goal of this project is to systematically extend the family of algebraic, numerical, and combinatorial techniques from the recent breakthroughs in Laplacian linear solvers and max-flows/min-cuts, to a wide-range of problems that arise in network analysis, data mining, and machine learning. This project aims to show that these techniques --- including advanced sampling, sparsification, and local exploration of networks --- will play increasing roles in improving algorithmic scalability. It contains several open questions and conjectures ranging from network analysis to distribution sampling to social influences towards this goal. By providing new algorithmic insights into various dynamic processes over graphs, the project also aims to improve the understanding of network facets beyond static graph structures in order to develop better algorithmic theory for network sciences.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.