Polystore mathematics of relational algebra

Financial transactions, internet search, and data analysis are all placing increasing demands on databases. SQL, NoSQL, and NewSQL databases have been developed to meet these demands and each offers unique benefits. SQL, NoSQL, and NewSQL databases also rely on different underlying mathematical models. Polystores seek to provide a mechanism to allow applications to transparently achieve the benefits of diverse databases while insulating applications from the details of these databases. Integrating the underlying mathematics of these diverse databases can be an important enabler for polystores as it enables effective reasoning across different databases. Associative arrays provide a common approach for the mathematics of polystores by encompassing the mathematics found in different databases: sets (SQL), graphs (NoSQL), and matrices (NewSQL). Prior work presented the SQL relational model in terms of associative arrays and identified key mathematical properties that are preserved within SQL. This work provides the rigorous mathematical definitions, lemmas, and theorems underlying these properties. Specifically, SQL Relational Algebra deals primarily with relations - multisets of tuples - and operations on and between those relations. These relations can be modeled as associative arrays by treating tuples as non-zero rows in an array. Operations in relational algebra are built as compositions of standard operations on associative arrays which mirror their matrix counterparts. These constructions provide insight into how relational algebra can be handled via array operations. As an example application, the composition of two projection operations is shown to also be a projection, and the projection of a union is shown to be equal to the union of the projections

Performance evaluation of an integrated RFI database for the MeerKAT/SKA radio telescope

For radio telescopes, radio frequency interference from terrestrial and other sources is a recognized problem that contaminates the signal (RFI) and must be tracked and ultimately removed. At the MeerKAT/SKA telescope, RFI is recorded with a variety of devices, including telescopes, sensors, and scanners; but the combination of data from these multiple sources to yield a unified view of RFI remains a challenging problem. Previously, we demonstrated that a scalable database model with an implementation based on the Polystore framework is a potential solution for RFI monitoring. Here we extend this work, implementing the database model in an integrated environment and evaluating its performance across a range of workloads with three data stores: SciDB, PSQL, and Accumulo. We find that SciDB and Accumulo scale better than PSQL under multi-user environments. Results show a minimal latency as low as 0.02 seconds, irrespective of the location, and data store type. Further, integrated APIs provide single notation and are 5% faster than third-party APIs. Our findings thus provide a guide to the proposed integrated RFI system at MeerKAT/SKA radio telescope

Polystore mathematics of relational algebra

Financial transactions, internet search, and data analysis are all placing increasing demands on databases. SQL, NoSQL, and NewSQL databases have been developed to meet these demands and each offers unique benefits. SQL, NoSQL, and NewSQL databases also rely on different underlying mathematical models. Polystores seek to provide a mechanism to allow applications to transparently achieve the benefits of diverse databases while insulating applications from the details of these databases. Integrating the underlying mathematics of these diverse databases can be an important enabler for polystores as it enables effective reasoning across different databases. Associative arrays provide a common approach for the mathematics of polystores by encompassing the mathematics found in different databases: sets (SQL), graphs (NoSQL), and matrices (NewSQL). Prior work presented the SQL relational model in terms of associative arrays and identified key mathematical properties that are preserved within SQL. This work provides the rigorous mathematical definitions, lemmas, and theorems underlying these properties. Specifically, SQL Relational Algebra deals primarily with relations - multisets of tuples - and operations on and between those relations. These relations can be modeled as associative arrays by treating tuples as non-zero rows in an array. Operations in relational algebra are built as compositions of standard operations on associative arrays which mirror their matrix counterparts. These constructions provide insight into how relational algebra can be handled via array operations. As an example application, the composition of two projection operations is shown to also be a projection, and the projection of a union is shown to be equal to the union of the projections

Multi-Temporal Analysis and Scaling Relations of 100,000,000,000 Network Packets

Our society has never been more dependent on computer networks. Effective utilization of networks requires a detailed understanding of the normal background behaviors of network traffic. Large-scale measurements of networks are computationally challenging. Building on prior work in interactive supercomputing and GraphBLAS hypersparse hierarchical traffic matrices, we have developed an efficient method for computing a wide variety of streaming network quantities on diverse time scales. Applying these methods to 100,000,000,000 anonymized source-destination pairs collected at a network gateway reveals many previously unobserved scaling relationships. These observations provide new insights into normal network background traffic that could be used for anomaly detection, AI feature engineering, and testing theoretical models of streaming networks.Comment: 6 pages, 6 figures,3 tables, 49 references, accepted to IEEE HPEC 202

HADAD: A Lightweight Approach for Optimizing Hybrid Complex Analytics Queries

International audienceHybrid complex analytics workloads typically include (i) data management tasks (joins, filters, etc.), easily expressed using relational algebra (RA)-based languages, and (ii) complex analytics tasks (regressions, matrix decompositions, etc.), mostly expressed in linear algebra (LA) expressions. Such workloads are common in a number of areas, including scientific computing, web analytics, business recommendation, natural language processing, speech recognition. Existing solutions for evaluating hybrid complex analytics queriesranging from LA-oriented systems, to relational systems (extended to handle LA operations), to hybrid systems-fail to provide a unified optimization framework for such a hybrid setting. These systems either optimize data management and complex analytics tasks separately, or exploit RA properties only while leaving LA-specific optimization opportunities unexplored. Finally, they are not able to exploit precomputed (materialized) results to avoid computing again (part of) a given mixed (LA and RA) computation. We describe HADAD, an extensible lightweight approach for optimizing hybrid complex analytics queries, based on a common abstraction that facilitates unified reasoning: a relational model endowed with integrity constraints, which can be used to express the properties of the two computation formalisms. Our approach enables full exploration of LA properties and rewrites, as well as semantic query optimization. Importantly, our approach does not require modifying the internals of the existing systems. Our experimental evaluation shows significant performance gains on diverse workloads, from LA-centered ones to hybrid ones

A cost-based storage format selector for materialized results in big data frameworks

Modern big data frameworks (such as Hadoop and Spark) allow multiple users to do large-scale analysis simultaneously, by deploying data-intensive workflows (DIWs). These DIWs of different users share many common tasks (i.e, 50–80%), which can be materialized and reused in future executions. Materializing the output of such common tasks improves the overall processing time of DIWs and also saves computational resources. Current solutions for materialization store data on Distributed File Systems by using a fixed storage format. However, a fixed choice is not the optimal one for every situation. Specifically, different layouts (i.e., horizontal, vertical or hybrid) have a huge impact on execution, according to the access patterns of the subsequent operations. In this paper, we present a cost-based approach that helps deciding the most appropriate storage format in every situation. A generic cost-based framework that selects the best format by considering the three main layouts is presented. Then, we use our framework to instantiate cost models for specific Hadoop storage formats (namely SequenceFile, Avro and Parquet), and test it with two standard benchmark suits. Our solution gives on average 1.33× speedup over fixed SequenceFile, 1.11× speedup over fixed Avro, 1.32× speedup over fixed Parquet, and overall, it provides 1.25× speedup.Peer ReviewedPostprint (author's final draft

Fast Queries Over Heterogeneous Data Through Engine Customization

Industry and academia are continuously becoming more data-driven and data-intensive, relying on the analysis of a wide variety of heterogeneous datasets to gain insights. The different data models and formats pose a significant challenge on performing analysis over a combination of diverse datasets. Serving all queries using a single, general-purpose query engine is slow. On the other hand, using a specialized engine for each heterogeneous dataset increases complexity: queries touching a combination of datasets require an integration layer over the different engines. This paper presents a system design that natively supports heterogeneous data formats and also minimizes query execution times. For multi-format support, the design uses an expressive query algebra which enables operations over various data models. For minimal execution times, it uses a code generation mechanism to mimic the system and storage most appropriate to answer a query fast. We validate our design by building Proteus, a query engine which natively supports queries over CSV, JSON, and relational binary data, and which specializes itself to each query, dataset, and workload via code generation. Proteus outperforms state-of-the-art open-source and commercial systems on both synthetic and real-world workloads without being tied to a single data model or format, all while exposing users to a single query interface

Efficient Latent Semantic Extraction from Cross Domain Data with Declarative Language

With large amounts of data continuously generated by intelligence devices, efficient analysis of huge data collections to unearth valuable insights has become one of the most elusive challenges for both academia and industry. The key elements to establishing a scalable analyzing framework should involve (1) an intuitive interface to describe the desired outcome, (2) a well-crafted model that integrates all available information sources to derive the optimal outcome and (3) an efficient algorithm that performs the data integration and extraction within a reasonable amount of time. In this dissertation, we address these challenges by proposing (1) a cross-language interface for a succinct expression of recursive queries, (2) a domain specific neural network model that can incorporate information of multiple modalities, and (3) a sample efficient training method that can be used even for extremely-large output-class classifiers. Our contributions in this thesis are thus threefold: First, for the ubiquitous recursive queries in advanced data analytics, on top of BigDatalog and Apache Spark, we design a succinct and expressive analytics tool encapsulating the functionality and classical algorithms of Datalog, a quintessential logic programming language. We provide the Logical Library (LLib), a Spark MLlib-like high-level API supporting a wide range of recursive algorithms and the Logical DataFrame (LFrame), an extension to Spark DataFrame supporting both relational and logical operations. The LLib and LFrame enable smooth collaborations between logical applications and other Spark libraries and cross-language logical programming in Scala, Java, or Python. Second, we utilize variants of recurrent neural network (RNN) to incorporate some enlightening sequential information overlooked by the conventional works in two different domains including Spoken Language Understanding (SLU) and Internet Embedding (IE). In SLU, we address the problem caused by solely relying on the first best interpretation (hypothesis) of an audio command through a series of new architectures comprising bidirectional LSTM and pooling layers to jointly utilize the other hypotheses' texts or embedding vectors, which are neglected but with valuable information missed by the first best hypothesis. In IE, we propose the DIP, an extension of RNN, to build up the internet coordinate system with the IP address sequences, which are also unnoticed in conventional distance-based internet embedding algorithms but encode structural information of the network. Both DIP and the integration of all hypotheses bring significant performance improvements for the corresponding downstream tasks. Finally, we investigate the training algorithm for multi-class classifiers with a large output-class size, which is common in deep neural networks and typically implemented as a softmax final layer with one output neuron per each class. To avoid expensive computing the intractable normalizing constant of softmax for each training data point, we analyze the well-known negative sampling and improve it to the amplified negative sampling algorithm, which gains much higher performance with lower training cost