Why is the snowflake schema a good data warehouse design?

Database design for data warehouses is based on the notion of the snowflake schema and its important special case, the star schema. The snowflake schema represents a dimensional model which is composed of a central fact table and a set of constituent dimension tables which can be further broken up into subdimension tables. We formalise the concept of a snowflake schema in terms of an acyclic database schema whose join tree satisfies certain structural properties. We then define a normal form for snowflake schemas which captures its intuitive meaning with respect to a set of functional and inclusion dependencies. We show that snowflake schemas in this normal form are independent as well as separable when the relation schemas are pairwise incomparable. This implies that relations in the data warehouse can be updated independently of each other as long as referential integrity is maintained. In addition, we show that a data warehouse in snowflake normal form can be queried by joining the relation over the fact table with the relations over its dimension and subdimension tables. We also examine an information-theoretic interpretation of the snowflake schema and show that the redundancy of the primary key of the fact table is zero

Provenance in Collaborative Data Sharing

This dissertation focuses on recording, maintaining and exploiting provenance information in Collaborative Data Sharing Systems (CDSS). These are systems that support data sharing across loosely-coupled, heterogeneous collections of relational databases related by declarative schema mappings. A fundamental challenge in a CDSS is to support the capability of update exchange --- which publishes a participant\u27s updates and then translates others\u27 updates to the participant\u27s local schema and imports them --- while tolerating disagreement between them and recording the provenance of exchanged data, i.e., information about the sources and mappings involved in their propagation. This provenance information can be useful during update exchange, e.g., to evaluate provenance-based trust policies. It can also be exploited after update exchange, to answer a variety of user queries, about the quality, uncertainty or authority of the data, for applications such as trust assessment, ranking for keyword search over databases, or query answering in probabilistic databases. To address these challenges, in this dissertation we develop a novel model of provenance graphs that is informative enough to satisfy the needs of CDSS users and captures the semantics of query answering on various forms of annotated relations. We extend techniques from data integration, data exchange, incremental view maintenance and view update to define the formal semantics of unidirectional and bidirectional update exchange. We develop algorithms to perform update exchange incrementally while maintaining provenance information. We present strategies for implementing our techniques over an RDBMS and experimentally demonstrate their viability in the Orchestra prototype system. We define ProQL, a query language for provenance graphs that can be used by CDSS users to combine data querying with provenance testing as well as to compute annotations for their data, based on their provenance, that are useful for a variety of applications. Finally, we develop a prototype implementation ProQL over an RDBMS and indexing techniques to speed up provenance querying, evaluate experimentally the performance of provenance querying and the benefits of our indexing techniques

Learning Models over Relational Data using Sparse Tensors and Functional Dependencies

Integrated solutions for analytics over relational databases are of great practical importance as they avoid the costly repeated loop data scientists have to deal with on a daily basis: select features from data residing in relational databases using feature extraction queries involving joins, projections, and aggregations; export the training dataset defined by such queries; convert this dataset into the format of an external learning tool; and train the desired model using this tool. These integrated solutions are also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This article introduces a unified framework for training and evaluating a class of statistical learning models over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from database theory such as schema information, query structure, functional dependencies, recent advances in query evaluation algorithms, and from linear algebra such as tensor and matrix operations, one can formulate relational analytics problems and design efficient (query and data) structure-aware algorithms to solve them. This theoretical development informed the design and implementation of the AC/DC system for structure-aware learning. We benchmark the performance of AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting and advertisement planning applications, AC/DC can learn polynomial regression models and factorization machines with at least the same accuracy as its competitors and up to three orders of magnitude faster than its competitors whenever they do not run out of memory, exceed 24-hour timeout, or encounter internal design limitations.Comment: 61 pages, 9 figures, 2 table

REX: Recursive, Delta-Based Data-Centric Computation

In today's Web and social network environments, query workloads include ad hoc and OLAP queries, as well as iterative algorithms that analyze data relationships (e.g., link analysis, clustering, learning). Modern DBMSs support ad hoc and OLAP queries, but most are not robust enough to scale to large clusters. Conversely, "cloud" platforms like MapReduce execute chains of batch tasks across clusters in a fault tolerant way, but have too much overhead to support ad hoc queries. Moreover, both classes of platform incur significant overhead in executing iterative data analysis algorithms. Most such iterative algorithms repeatedly refine portions of their answers, until some convergence criterion is reached. However, general cloud platforms typically must reprocess all data in each step. DBMSs that support recursive SQL are more efficient in that they propagate only the changes in each step -- but they still accumulate each iteration's state, even if it is no longer useful. User-defined functions are also typically harder to write for DBMSs than for cloud platforms. We seek to unify the strengths of both styles of platforms, with a focus on supporting iterative computations in which changes, in the form of deltas, are propagated from iteration to iteration, and state is efficiently updated in an extensible way. We present a programming model oriented around deltas, describe how we execute and optimize such programs in our REX runtime system, and validate that our platform also handles failures gracefully. We experimentally validate our techniques, and show speedups over the competing methods ranging from 2.5 to nearly 100 times.Comment: VLDB201

Efficient Incremental View Maintenance for Data Warehousing

Data warehousing and on-line analytical processing (OLAP) are essential elements for decision support applications. Since most OLAP queries are complex and are often executed over huge volumes of data, the solution in practice is to employ materialized views to improve query performance. One important issue for utilizing materialized views is to maintain the view consistency upon source changes. However, most prior work focused on simple SQL views with distributive aggregate functions, such as SUM and COUNT. This dissertation proposes to consider broader types of views than previous work. First, we study views with complex aggregate functions such as variance and regression. Such statistical functions are of great importance in practice. We propose a workarea function model and design a generic framework to tackle incremental view maintenance and answering queries using views for such functions. We have implemented this approach in a prototype system of IBM DB2. An extensive performance study shows significant performance gains by our techniques. Second, we consider materialized views with PIVOT and UNPIVOT operators. Such operators are widely used for OLAP applications and for querying sparse datasets. We demonstrate that the efficient maintenance of views with PIVOT and UNPIVOT operators requires more generalized operators, called GPIVOT and GUNPIVOT. We formally define and prove the query rewriting rules and propagation rules for such operators. We also design a novel view maintenance framework for applying these rules to obtain an efficient maintenance plan. Extensive performance evaluations reveal the effectiveness of our techniques. Third, materialized views are often integrated from multiple data sources. Due to source autonomicity and dynamicity, concurrency may occur during view maintenance. We propose a generic concurrency control framework to solve such maintenance anomalies. This solution extends previous work in that it solves the anomalies under both source data and schema changes and thus achieves full source autonomicity. We have implemented this technique in a data warehouse prototype developed at WPI. The extensive performance study shows that our techniques put little extra overhead on existing concurrent data update processing techniques while allowing for this new functionality