AF:III:Small:Collaborative Research: New Frontiers in Join Algorithms: Optimality, Noise, and Richer Languages

关系连接是关系数据库处理的核心，关系数据库处理是当今处理数据的主要方式。本书还对生物和社会网络、编码理论、压缩感知、机器学习和约束满足等问题进行了建模。最近，研究人员描述了连接查询的第一个最坏情况最优算法（NPRR算法）。这些新结果开辟了一系列新工具，用于解决与连接相关的各种基本问题。本项目旨在进一步利用为NPRR开发的新算法技术来解决以下三类问题：(1)最优连接算法。当数据存储在传统数据库索引或新的索引结构中时，开发实例最优的算法是这个项目的目标。(2)应对和利用噪音。该项目将扩展最新的工作，以处理和利用最坏情况和统计噪声模型，连接编码理论和压缩感知。(3)表达性查询语言。该项目将探索一系列连接查询的扩展，这些扩展将为克服motif查找、搜索、具有功能依赖的数据库以及更强大的查询类和连接操作等方面的挑战铺平道路。如果获得成功，该资助的结果将适用于现代大规模、动态和噪声数据集中的各种模式提取问题，这些数据集在复杂网络分析、编码理论和压缩感知方面具有广泛的应用。

The relational join is central to relational database processing, which is the dominant way data is processed today. The join also models problems in biological and social networks, coding theory, compressed sensing, machine learning, and constraint satisfaction. Recently,  the investigators described the first ever worst-case optimal algorithm (the NPRR algorithm) for join queries.  These new results open a line of new tools to attack a diverse set of fundamental problems related to the join. This project aims to further exploit the new algorithmic techniques developed for NPRR to address the following three classes of problems:(1) Optimal Join algorithms. Developing algorithms that are instance optimal when the data are stored in either traditional database indexes or new indexing structures is a goal of this project. (2) Coping with and Leveraging Noise. This project will extend the latest work to handle and leverage both worst-case and statistical noise models, bridging to coding theory and compressed sensing.  (3) Expressive Query Languages. The project will explore a series of extensions to join queries that will pave the way to overcome challenges in motif finding, search, databases with functional dependencies, and more powerful classes of queries and join operations.If successful, the results of this grant will apply to a variety of pattern extraction problems in modern massive, dynamic, and noisy data sets, which have a wide range of applications in complex network analysis, coding theory, and compressive sensing.