AF: Small: Scalable Algorithms for Data and Network Analysis

AF：小型：用于数据和网络分析的可扩展算法

• 批准号: 1815254
• 负责人: Shanghua Teng
• 金额: $ 50万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-06-01 至 2022-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1815254&HistoricalAwards=false
• 关键词: AF; Small; Scalable; Algorithms; Data

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.

涉及大输入数据集的基于数据的决策需要算法花费大量时间来处理它们。在计算机科学中，高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。 “可扩展算法”是最有效的算法之一，因为它们的运行时间要求与问题规模接近线性甚至亚线性。换句话说，当输入大小扩大时，它们的复杂性会优雅地扩展。在大数据时代，对高效算法的需求比以往任何时候都更高。虽然大数据将我们带入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对高效算法的经典概念提出了重大挑战：根据传统多项式时间表征，过去被认为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，应将可扩展性而不是多项式时间可计算性提升为表征高效计算的核心复杂性概念，这将成为网络科学和大数据算法设计的重点。该项目将专注于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（例如可扩展性），尊重这些学科研究人员对大数据时代实用算法的敏感性，该项目旨在提高理论分析对这些领域研究人员的价值。 由于该项目将多个学科的想法结合在一项连贯的研究工作中，因此关于该项目成果的讲座和教程将有助于在其范围内交叉促进各学科的发展。 可能具有实际应用性的理论算法的开发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启发式方法。这项研究的跨学科性质将使网络科学、机器学习、数值分析和社会科学领域的博士生和研究人员能够更广泛地参与，从而增加成功支持女性和少数族裔研究人员并与之合作的机会。该项目的技术目标是系统地扩展代数、数值和组合技术的家族，这些技术来自拉普拉斯线性求解器的最新突破和 最大流/最小割，解决网络分析、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、稀疏化和网络局部探索）将在提高算法可扩展性方面发挥越来越重要的作用。 它包含几个悬而未决的问题和猜想，从网络分析到分布抽样再到对这一目标的社会影响。 通过为图上的各种动态过程提供新的算法见解，该项目还旨在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智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Quantum-Inspired Combinatorial Games: Algorithms and Complexity

受量子启发的组合游戏：算法和复杂性

• DOI: 10.4230/lipics.fun.2022.11
• 发表时间: 2022
• 期刊: Fun with Algorithms
• 作者: Kyle G. Burke;Matthew Ferland;S. Teng
• 通讯作者: S. Teng

Computational Analyses of the Electoral College: Campaigning Is Hard But Approximately Manageable

选举团的计算分析：竞选活动很困难，但大致可控

• DOI: 10.1609/aaai.v35i6.16668
• 发表时间: 2021
• 期刊: Proceedings of the AAAI Conference on Artificial Intelligence
• 作者: Dehghani, Sina;Saleh, Hamed;Seddighin, Saeed;Teng, Shang-Hua
• 通讯作者: Teng, Shang-Hua

A graph-theoretical basis of stochastic-cascading network influence: Characterizations of influence-based centrality

• DOI: 10.1016/j.tcs.2020.04.016
• 发表时间: 2020-07
• 期刊: Theor. Comput. Sci.
• 作者: Wei Chen;S. Teng;Hanrui Zhang

Winning the War by (Strategically) Losing Battles: Settling the Complexity of Grundy-Values in Undirected Geography

通过（战略上）失败来赢得战争：解决无向地理中格兰迪价值观的复杂性

• DOI: 10.1109/focs52979.2021.00119
• 发表时间: 2021
• 期刊: IEEE Annual Symposium on Foundations of Computer Science
• 作者: Kyle G. Burke;Matthew Ferland;S. Teng
• 通讯作者: S. Teng

Optimal Space-Depth Trade-Off of CNOT Circuits in Quantum Logic Synthesis.

量子逻辑综合中 CNOT 电路的最佳空间深度权衡。

• 发表时间: 2020
• 期刊: Proceedings of the annual ACMSIAM symposium on discrete algorithms
• 作者: Jiang, Jiaqing;Sun, Xiaoming;Teng, Shang-Hua;Wu, Bujiao;Wu, Kewen;Zhang, Jialin
• 通讯作者: Zhang, Jialin