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.
