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Register a new userTyped Linear Algebra for Efficient Analytical Querying
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Jose Oliveira Prof
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of expressing queries (paths in LA diagrams). A kernel of LA operators has been implemented so that paths extracted from LA diagrams can be executed. The approach is validated and evaluated taking TPC-H benchmark queries as reference. The performance of the LA-based approach is compared with popular database competitors (PostgreSQL and MySQL).
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In ontology-mediated querying, description logic (DL) ontologies are used to enrich incomplete data with domain knowledge which results in more complete answers to queries. However, the evaluation of ontology-mediated queries (OMQs) over relational databases is computationally hard. This raises the question when OMQ evaluation is efficient, in the sense of being tractable in combined complexity or fixed-parameter tractable. We study this question for a range of ontology-mediated query languages based on several important and widely-used DLs, using unions of conjunctive queries as the actual queries. For the DL ELHI extended with the bottom concept, we provide a characterization of the classes of OMQs that are fixed-parameter tractable. For its fragment EL extended with domain and range restrictions and the bottom concept (which restricts the use of inverse roles), we provide a characterization of the classes of OMQs that are tractable in combined complexity. Both results are in terms of equivalence to OMQs of bounded tree width and rest on a reasonable assumption from parameterized complexity theory. They are similar in spirit to Grohes seminal characterization of the tractable classes of conjunctive queries over relational databases. We further study the complexity of the meta problem of deciding whether a given OMQ is equivalent to an OMQ of bounded tree width, providing several completeness results that range from NP to 2ExpTime, depending on the DL used. We also consider the DL-Lite family of DLs, including members that admit functional roles.
We present here a formal foundation for an iterative and incremental approach to constructing and evaluating preference queries. Our main focus is on query modification: a query transformation approach which works by revising the preference relation in the query. We provide a detailed analysis of the cases where the order-theoretic properties of the preference relation are preserved by the revision. We consider a number of different revision operators: union, prioritized and Pareto composition. We also formulate algebraic laws that enable incremental evaluation of preference queries. Finally, we consider two variations of the basic framework: finite restrictions of preference relations and weak-order extensions of strict partial order preference relations.
Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common subexpressions and fusible operators. The complex interaction among these properties impact on the execution cost poses a challenge to optimizing compilers. Existing compilers resort to intricate heuristics that complicate the codebase and add maintenance cost but fail to search through the large space of equivalent LA expressions to find the cheapest one. We introduce a general optimization technique for LA expressions, by converting the LA expressions into Relational Algebra (RA) expressions, optimizing the latter, then converting the result back to (optimized) LA expressions. One major advantage of this method is that it is complete, meaning that any equivalent LA expression can be found using the equivalence rules in RA. The challenge is the major size of the search space, and we address this by adopting and extending a technique used in compilers, called equality saturation. We integrate the optimizer into SystemML and validate it empirically across a spectrum of machine learning tasks; we show that we can derive all existing hand-coded optimizations in SystemML, and perform new optimizations that lead to speedups from 1.2X to 5X.
Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL. The latter are object of study in the present paper. For this purpose, a core graph query language GrAL is defined with focus on CONSTRUCT queries. Queries in GrAL form the final step of a recursive process involving so-called GrAL patterns. By evaluating a query over a graph one gets a graph, while by evaluating a pattern over a graph one gets a set of matches which involves both a graph and a table. CONSTRUCT queries are based on CONSTRUCT patterns, and sub-CONSTRUCT patterns come for free from the recursive definition of patterns. The semantics of GrAL is based on RDF graphs with a slight modification which consists in accepting isolated nodes. Such an extension of RDF graphs eases the definition of the evaluation semantics, which is mainly captured by a unique operation called Merge. Besides, we define aggregations as part of GrAL expressions, which leads to an original local processing of aggregations.
Significant efforts have been expended in the research and development of a database management system (DBMS) that has a wide range of applications for managing an enormous collection of multisource, heterogeneous, complex, or growing data. Besides the primary function (i.e., create, delete, and update), a practical and impeccable DBMS can interact with users through information selection, that is, querying with their targets. Previous querying algorithms, such as frequent itemset querying and sequential pattern querying (SPQ) have focused on the measurement of frequency, which does not involve the concept of utility, which is helpful for users to discover more informative patterns. To apply the querying technology for wider applications, we incorporate utility into target-oriented SPQ and formulate the task of targeted utility-oriented sequence querying. To address the proposed problem, we develop a novel algorithm, namely targeted high-utility sequence querying (TUSQ), based on two novel upper bounds suffix remain utility and terminated descendants utility as well as a vertical Last Instance Table structure. For further efficiency, TUSQ relies on a projection technology utilizing a compact data structure called the targeted chain. An extensive experimental study conducted on several real and synthetic datasets shows that the proposed algorithm outperformed the designed baseline algorithm in terms of runtime, memory consumption, and candidate filtering.
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