Lower Bounds for Oblivious Near-Neighbor Search

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search ($\mathsf{ANN}$) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for $\mathsf{ANN}$. This is the first super-logarithmic $\mathit{unconditional}$ lower bound for $\mathsf{ANN}$ against general (non black-box) data structures. We also show that any oblivious $\mathit{static}$ data structure for decomposable search problems (like $\mathsf{ANN}$) can be obliviously dynamized with $O(\log n)$ overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page

Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space

For a set of $n$ points in $\Re^d$, and parameters $k$ and \eps, we present a data structure that answers (1+\eps,k)-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is \Otilde (n /k); that is, the space used is sublinear in the input size if $k$ is sufficiently large. Our approach provides a novel way to summarize geometric data, such that meaningful proximity queries on the data can be carried out using this sketch. Using this, we provide a sublinear space data-structure that can estimate the density of a point set under various measures, including: \begin{inparaenum}[(i)] \item sum of distances of $k$ closest points to the query point, and \item sum of squared distances of $k$ closest points to the query point. \end{inparaenum} Our approach generalizes to other distance based estimation of densities of similar flavor. We also study the problem of approximating some of these quantities when using sampling. In particular, we show that a sample of size \Otilde (n /k) is sufficient, in some restricted cases, to estimate the above quantities. Remarkably, the sample size has only linear dependency on the dimension

A framework for multidimensional indexes on distributed and highly-available data stores

Spatial Big Data is considered an essential trend in future scientific and business applications. Indeed, research instruments, medical devices, and social networks generate hundreds of peta bytes of spatial data per year. However, as many authors have pointed out, the lack of specialized frameworks dealing with such kind of data is limiting possible applications and probably precluding many scientific breakthroughs. In this thesis, we describe three HPC scientific applications, ranging from molecular dynamics, neuroscience analysis, and physics simulations, where we experience first hand the limits of the existing technologies. Thanks to our experience, we define the desirable missing functionalities, and we focus on two features that when combined significantly improve the way scientific data is analyzed. On one side, scientific simulations generate complex datasets where multiple correlated characteristics describe each item. For instance, a particle might have a space position (x,y,z) at a given time (t). If we want to find all elements within the same area and period, we either have to scan the whole dataset, or we must organize the data so that all items in the same space and time are stored together. The second approach is called Multidimensional Indexing (MI), and it uses different techniques to cluster and to organize similar data together. On the other side, approximate analytics has been often indicated as a smart and flexible way to explore large datasets in a short period. Approximate analytics includes a broad family of algorithms which aims to speed up analytical workloads by relaxing the precision of the results within a specific interval of confidence. For instance, if we want to know the average age in a group with 1-year precision, we can consider just a random fraction of all the people, thus reducing the amount of calculation. But if we also want less I/O operations, we need efficient data sampling, which means organizing data in a way that we do not need to scan the whole data set to generate a random sample of it. According to our analysis, combining Multidimensional Indexing with efficient data Sampling (MIS) is a vital missing feature not available in the current distributed data management solutions. This thesis aims to solve such a shortcoming and it provides novel scalable solutions. At first, we describe the existing data management alternatives; then we motivate our preference for NoSQL key-value databases. Secondly, we propose an analytical model to study the influence of data models on the scalability and performance of this kind of distributed database. Thirdly, we use the analytical model to design two novel multidimensional indexes with efficient data sampling: the D8tree and the AOTree. Our first solution, the D8tree, improves state of the art for approximate spatial queries on static and mostly read dataset. Later, we enhanced the data ingestion capability or our approach by introducing the AOTree, an algorithm that enables the query performance of the D8tree even for HPC write-intensive applications. We compared our solution with PostgreSQL and plain storage, and we demonstrate that our proposal has better performance and scalability. Finally, we describe Qbeast, the novel distributed system that implements the D8tree and the AOTree using NoSQL technologies, and we illustrate how Qbeast simplifies the workflow of scientists in various HPC applications providing a scalable and integrated solution for data analysis and management.La gestión de BigData con información espacial está considerada como una tendencia esencial en el futuro de las aplicaciones científicas y de negocio. De hecho, se generan cientos de petabytes de datos espaciales por año mediante instrumentos de investigación, dispositivos médicos y redes sociales. Sin embargo, tal y como muchos autores han señalado, la falta de entornos especializados en manejar este tipo de datos está limitando sus posibles aplicaciones y está impidiendo muchos avances científicos. En esta tesis, describimos 3 aplicaciones científicas HPC, que cubren los ámbitos de dinámica molecular, análisis neurocientífico y simulaciones físicas, donde hemos experimentado en primera mano las limitaciones de las tecnologías existentes. Gracias a nuestras experiencias, hemos podido definir qué funcionalidades serían deseables y no existen, y nos hemos centrado en dos características que, al combinarlas, mejoran significativamente la manera en la que se analizan los datos científicos. Por un lado, las simulaciones científicas generan conjuntos de datos complejos, en los que cada elemento es descrito por múltiples características correlacionadas. Por ejemplo, una partícula puede tener una posición espacial (x, y, z) en un momento dado (t). Si queremos encontrar todos los elementos dentro de la misma área y periodo, o bien recorremos y analizamos todo el conjunto de datos, o bien organizamos los datos de manera que se almacenen juntos todos los elementos que comparten área en un momento dado. Esta segunda opción se conoce como Indexación Multidimensional (IM) y usa diferentes técnicas para agrupar y organizar datos similares. Por otro lado, se suele señalar que las analíticas aproximadas son una manera inteligente y flexible de explorar grandes conjuntos de datos en poco tiempo. Este tipo de analíticas incluyen una amplia familia de algoritmos que acelera el tiempo de procesado, relajando la precisión de los resultados dentro de un determinado intervalo de confianza. Por ejemplo, si queremos saber la edad media de un grupo con precisión de un año, podemos considerar sólo un subconjunto aleatorio de todas las personas, reduciendo así la cantidad de cálculo. Pero si además queremos menos operaciones de entrada/salida, necesitamos un muestreo eficiente de datos, que implica organizar los datos de manera que no necesitemos recorrerlos todos para generar una muestra aleatoria. De acuerdo con nuestros análisis, la combinación de Indexación Multidimensional con Muestreo eficiente de datos (IMM) es una característica vital que no está disponible en las soluciones actuales de gestión distribuida de datos. Esta tesis pretende resolver esta limitación y proporciona unas soluciones novedosas que son escalables. En primer lugar, describimos las alternativas de gestión de datos que existen y motivamos nuestra preferencia por las bases de datos NoSQL basadas en clave-valor. En segundo lugar, proponemos un modelo analítico para estudiar la influencia que tienen los modelos de datos sobre la escalabilidad y el rendimiento de este tipo de bases de datos distribuidas. En tercer lugar, usamos el modelo analítico para diseñar dos novedosos algoritmos IMM: el D8tree y el AOTree. Nuestra primera solución, el D8tree, mejora el estado del arte actual para consultas espaciales aproximadas, cuando el conjunto de datos es estático y mayoritariamente de lectura. Después, mejoramos la capacidad de ingestión introduciendo el AOTree, un algoritmo que conserva el rendimiento del D8tree incluso para aplicaciones HPC intensivas en escritura. Hemos comparado nuestra solución con PostgreSQL y almacenamiento plano demostrando que nuestra propuesta mejora tanto el rendimiento como la escalabilidad. Finalmente, describimos Qbeast, el sistema que implementa los algoritmos D8tree y AOTree, e ilustramos cómo Qbeast simplifica el flujo de trabajo de los científicos ofreciendo una solución escalable e integraPostprint (published version

Scalable aggregation predictive analytics: a query-driven machine learning approach

We introduce a predictive modeling solution that provides high quality predictive analytics over aggregation queries in Big Data environments. Our predictive methodology is generally applicable in environments in which large-scale data owners may or may not restrict access to their data and allow only aggregation operators like COUNT to be executed over their data. In this context, our methodology is based on historical queries and their answers to accurately predict ad-hoc queries’ answers. We focus on the widely used set-cardinality, i.e., COUNT, aggregation query, as COUNT is a fundamental operator for both internal data system optimizations and for aggregation-oriented data exploration and predictive analytics. We contribute a novel, query-driven Machine Learning (ML) model whose goals are to: (i) learn the query-answer space from past issued queries, (ii) associate the query space with local linear regression & associative function estimators, (iii) define query similarity, and (iv) predict the cardinality of the answer set of unseen incoming queries, referred to the Set Cardinality Prediction (SCP) problem. Our ML model incorporates incremental ML algorithms for ensuring high quality prediction results. The significance of contribution lies in that it (i) is the only query-driven solution applicable over general Big Data environments, which include restricted-access data, (ii) offers incremental learning adjusted for arriving ad-hoc queries, which is well suited for query-driven data exploration, and (iii) offers a performance (in terms of scalability, SCP accuracy, processing time, and memory requirements) that is superior to data-centric approaches. We provide a comprehensive performance evaluation of our model evaluating its sensitivity, scalability and efficiency for quality predictive analytics. In addition, we report on the development and incorporation of our ML model in Spark showing its superior performance compared to the Spark’s COUNT method

CubiST++: Evaluating Ad-Hoc CUBE Queries Using Statistics Trees

We report on a new, efficient encoding for the data cube, which results in a drastic speed-up of OLAP queries that aggregate along any combination of dimensions over numerical and categorical attributes. We are focusing on a class of queries called cube queries, which return aggregated values rather than sets of tuples. Our approach, termed CubiST++ (Cubing with Statistics Trees Plus Families), represents a drastic departure from existing relational (ROLAP) and multi-dimensional (MOLAP) approaches in that it does not use the view lattice to compute and materialize new views from existing views in some heuristic fashion. Instead, CubiST++ encodes all possible aggregate views in the leaves of a new data structure called statistics tree (ST) during a one-time scan of the detailed data. In order to optimize the queries involving constraints on hierarchy levels of the underlying dimensions, we select and materialize a family of candidate trees, which represent superviews over the different hierarchical levels of the dimensions. Given a query, our query evaluation algorithm selects the smallest tree in the family, which can provide the answer. Extensive evaluations of our prototype implementation have demonstrated its superior run-time performance and scalability when compared with existing MOLAP and ROLAP systems