On Defining SPARQL with Boolean Tensor Algebra

The Resource Description Framework (RDF) represents information as subject-predicate-object triples. These triples are commonly interpreted as a directed labelled graph. We propose an alternative approach, interpreting the data as a 3-way Boolean tensor. We show how SPARQL queries - the standard queries for RDF - can be expressed as elementary operations in Boolean algebra, giving us a complete re-interpretation of RDF and SPARQL. We show how the Boolean tensor interpretation allows for new optimizations and analyses of the complexity of SPARQL queries. For example, estimating the size of the results for different join queries becomes much simpler

Fast and Simple Relational Processing of Uncertain Data

This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra extended by an operation for computing possible answers, a query on the logical level can be translated into, and evaluated as, a single relational algebra query on the U-relation representation. The translation scheme essentially preserves the size of the query in terms of number of operations and, in particular, number of joins. Standard techniques employed in off-the-shelf relational database management systems are effective for optimizing and processing queries on U-relations. In our experiments we show that query evaluation on U-relations scales to large amounts of data with high degrees of uncertainty.Comment: 12 pages, 14 figure

Schema Independent Relational Learning

Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability. Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency. This variation complicates their off-the-shelf application. In this paper, we introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We study both sample-based learning algorithms, which learn from sets of labeled examples, and query-based algorithms, which learn by asking queries to an oracle. We prove that current relational learning algorithms are generally not schema independent. For query-based learning algorithms we show that the (de) composition transformations influence their query complexity. We propose Castor, a sample-based relational learning algorithm that achieves schema independence by leveraging data dependencies. We support the theoretical results with an empirical study that demonstrates the schema dependence/independence of several algorithms on existing benchmark and real-world datasets under (de) compositions

Provenance Circuits for Trees and Treelike Instances (Extended Version)

Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such as counting query results [3] or performing query evaluation on probabilistic trees [10]. These are two examples of the more general problem of computing augmented query output, that is referred to as provenance. This article presents a provenance framework for trees and treelike instances, by describing a linear-time construction of a circuit provenance representation for MSO queries. We show how this provenance can be connected to the usual definitions of semiring provenance on relational instances [20], even though we compute it in an unusual way, using tree automata; we do so via intrinsic definitions of provenance for general semirings, independent of the operational details of query evaluation. We show applications of this provenance to capture existing counting and probabilistic results on trees and treelike instances, and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1

Compressed Representations of Conjunctive Query Results

Relational queries, and in particular join queries, often generate large output results when executed over a huge dataset. In such cases, it is often infeasible to store the whole materialized output if we plan to reuse it further down a data processing pipeline. Motivated by this problem, we study the construction of space-efficient compressed representations of the output of conjunctive queries, with the goal of supporting the efficient access of the intermediate compressed result for a given access pattern. In particular, we initiate the study of an important tradeoff: minimizing the space necessary to store the compressed result, versus minimizing the answer time and delay for an access request over the result. Our main contribution is a novel parameterized data structure, which can be tuned to trade off space for answer time. The tradeoff allows us to control the space requirement of the data structure precisely, and depends both on the structure of the query and the access pattern. We show how we can use the data structure in conjunction with query decomposition techniques, in order to efficiently represent the outputs for several classes of conjunctive queries.Comment: To appear in PODS'18; 35 pages; comments welcom

Representation Independent Analytics Over Structured Data

Database analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural properties observed over particular representations do not necessarily hold for alternative structures. Thus, there is no guarantee that current database analytics algorithms will still provide the correct insights, no matter what structures are chosen to organize the database. Because these algorithms tend to be highly effective over some choices of structure, such as that of the databases used to validate them, but not so effective with others, database analytics has largely remained the province of experts who can find the desired forms for these algorithms. We argue that in order to make database analytics usable, we should use or develop algorithms that are effective over a wide range of choices of structural organizations. We introduce the notion of representation independence, study its fundamental properties for a wide range of data analytics algorithms, and empirically analyze the amount of representation independence of some popular database analytics algorithms. Our results indicate that most algorithms are not generally representation independent and find the characteristics of more representation independent heuristics under certain representational shifts