Tool for SPARQL Querying over Compact RDF Representations

Presented at the 4th XoveTIC Conference, A Coruña, Spain, 7–8 October 2021.[Abstract] We present an architecture for the efficient storing and querying of large RDF datasets. Our approach seeks to store RDF datasets in very little space while offering complete SPARQL functionality. To achieve this, our proposal was built over HDT, an RDF serialization framework, and its interaction with the Jena query engine. We propose a set of modifications to this framework in order to incorporate a range of space-efficient compact data structures for data storage and access, while using high-level capabilities to answer more complicated SPARQL queries. As a result, our approach provides a standard mechanism for using low-level data structures in complicated query situations requiring SPARQL searches, which are typically not supported by current solutions.This research was funded by Xunta de Galicia/FEDER grant ED431G 2019/01, Xunta de Galicia/FEDER-UE grant IN852A 2018/14; Ministerio de Ciencia, Innovación y Universidades grants [TIN2016-78011-C4-1-R; PID2019-105221RB-C41]; Consellería de Cultura, Educación e Universidade/Consellería de Economía, Empresa e Innovación/GAIN/Xunta de Galicia grant ED431C 2021/53; and by MICINN (PGE/ERDF) grant PID2020-114635RB-I00.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; IN852A 2018/14Xunta de Galicia; ED431C 2021/5

New data structures and algorithms for the efficient management of large spatial datasets

[Resumen] En esta tesis estudiamos la representación eficiente de matrices multidimensionales, presentando nuevas estructuras de datos compactas para almacenar y procesar grids en distintos ámbitos de aplicación. Proponemos varias estructuras de datos estáticas y dinámicas para la representación de matrices binarias o de enteros y estudiamos aplicaciones a la representación de datos raster en Sistemas de Información Geográfica, bases de datos RDF, etc. En primer lugar proponemos una colección de estructuras de datos estáticas para la representación de matrices binarias y de enteros: 1) una nueva representación de matrices binarias con grandes grupos de valores uniformes, con aplicaciones a la representación de datos raster binarios; 2) una nueva estructura de datos para representar matrices multidimensionales; 3) una nueva estructura de datos para representar matrices de enteros con soporte para consultas top-k de rango. También proponemos una nueva representación dinámica de matrices binarias, una nueva estructura de datos que proporciona las mismas funcionalidades que nuestras propuestas estáticas pero también soporta cambios en la matriz. Nuestras estructuras de datos pueden utilizarse en distintos dominios. Proponemos variantes específicas y combinaciones de nuestras propuestas para representar grafos temporales, bases de datos RDF, datos raster binarios o generales y datos raster temporales. También proponemos un nuevo algoritmo para consultar conjuntamente un conjuto de datos raster (almacenado usando nuestras propuestas) y un conjunto de datos vectorial almacenado en una estructura de datos clásica, mostrando que nuestra propuesta puede ser más rápida y usar menos espacio que otras alternativas. Nuestras representaciones proporcionan interesantes trade-offs y son competitivas en espacio y tiempos de consulta con representaciones habituales en los diferentes dominios.[Resumo] Nesta tese estudiamos a representación eficiente de matrices multidimensionais, presentando novas estruturas de datos compactas para almacenar e procesar grids en distintos ámbitos de aplicación. Propoñemos varias estruturas de datos estáticas e dinámicas para a representación de matrices binarias ou de enteiros e estudiamos aplicacións á representación de datos raster en Sistemas de Información Xeográfica, bases de datos RDF, etc. En primeiro lugar propoñemos unha colección de estruturas de datos estáticas para a representación de matrices binarias e de enteiros: 1) unha nova representación de matrices binarias con grandes grupos de valores uniformes, con aplicacións á representación de datos raster binarios; 2) unha nova estrutura de datos para representar matrices multidimensionais; 3) unha nova estrutura de datos para representar matrices de enteiros con soporte para consultas top-k. Tamén propoñemos unha nova representación dinámica de matrices binarias, unha nova estrutura de datos que proporciona as mesmas funcionalidades que as nosas propostas estáticas pero tamén soporta cambios na matriz. As nosas estruturas de datos poden utilizarse en distintos dominios. Propoñemos variantes específicas e combinacións das nosas propostas para representar grafos temporais, bases de datos RDF, datos raster binarios ou xerais e datos raster temporais. Tamén propoñemos un novo algoritmo para consultar conxuntamente datos raster (almacenados usando as nosas propostas) con datos vectoriais almacenados nunha estrutura de datos clásica, amosando que a nosa proposta pode ser máis rápida e usar menos espazo que outras alternativas. As nosas representacións proporcionan interesantes trade-offs e son competitivas en espazo e tempos de consulta con representacións habituais nos diferentes dominios.[Abstract] In this thesis we study the efficient representation of multidimensional grids, presenting new compact data structures to store and query grids in different application domains. We propose several static and dynamic data structures for the representation of binary grids and grids of integers, and study applications to the representation of raster data in Geographic Information Systems, RDF databases, etc. We first propose a collection of static data structures for the representation of binary grids and grids of integers: 1) a new representation of bi-dimensional binary grids with large clusters of uniform values, with applications to the representation of binary raster data; 2) a new data structure to represent multidimensional binary grids; 3) a new data structure to represent grids of integers with support for top-k range queries. We also propose a new dynamic representation of binary grids, a new data structure that provides the same functionalities that our static representations of binary grids but also supports changes in the grid. Our data structures can be used in several application domains. We propose specific variants and combinations of our generic proposals to represent temporal graphs, RDF databases, OLAP databases, binary or general raster data, and temporal raster data. We also propose a new algorithm to jointly query a raster dataset (stored using our representations) and a vectorial dataset stored in a classic data structure, showing that our proposal can be faster and require less space than the usual alternatives. Our representations provide interesting trade-offs and are competitive in terms of space and query times with usual representations in the different domains

Weak convergence of varying measures and Hermite-Padé orthogonal polynomials

23 pages, no figures.-- MSC1991 codes: 42C05, 30E10.MR#: MR1702795 (2000j:42036)Zbl#: Zbl 1058.42503It is known that the common denominator of the Hermite-Padé approximants of a mixed Angelesco-Nikishin system shares orthogonality relations with respect to each function in the system. It is less well known that they also satisfy full orthogonality with respect to a varying measure. This problem motivates our interest in extending the class of varying measures with respect to which weak asymptotics of orthogonal polynomials takes place. In particular, for the case of a Nikishin system, we prove weak asymptotics of the corresponding varying measures.Research by second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad

Strong asymptotics for orthogoal polynomials with varying measures and Hermite-Padé approximants

13 pages, no figures.-- MSC1991 codes: 42C05; 30E10.-- Issue title: "Proceedings of the VIIIth Symposium on Orthogonal Polynomials and Their Application" (Seville, Spain, Sep. 1997), edited by Antonio J. Durán.MR#: MR1662686 (99i:42035)Zbl#: Zbl 0933.42017The strong asymptotic behaviour of orthogonal polynomials with respect to a general class of varying measures is given for the case of the unit circle and the real line. These results are used to obtain certain asymptotic relations for the polynomials involved in the construction of Hermite-Padé approximants of a Nikishin system of functions.The research of the second author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad

Convergence of multipoint Padé-type approximants

22 pages, no figures.-- MSC2000 code: 41A21.MR#: MR1820896 (2002a:41014)Zbl#: Zbl 0982.41008Let μ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in \bbfC\setminus I\$ and r(\infty)=0$. We consider multipoint rational interpolants of the function$$f(z)=\int {d\mu(x)\over z-x}+r(z)$$, where some poles are fixed and others are left free. We show that if the interpolation points and the fixed poles are chosen conveniently then the sequence of multipoint rational approximants converges geometrically to f in the chordal metric on compact subsets of$\bbfC\setminus I\$.The second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01 and by INTAS under Grant 93-0219 EXT.Publicad

Convergencia relativa de polinomios ortogonales variantes

12 pages, no figures.-- MSC2000 codes: Primary: 42C05, 30E15; Secondary: 30E10.We consider the relative asymptotic behaviour of orthogonal polynomials with respect to varying measures supported on the real line and the unit circle. The main feature of the results is the generality of the class of measures studied.El trabajo de los dos autores ha sido parcialmente financiado por la Dirección General de Investigación, Ministerio de Ciencia y Tecnología, a través del proyecto BFM2000-0206-C04-01 y además, en el caso de G. López, por el INTAS.Publicad

Stieltjes-type polynomials on the unit circle

29 pages, no figures.-- MSC2000 codes: Primary 65D32, 42A10, 42C05; Secondary 30E20.MR#: MR2476567Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of convergence of certain quadrature formulae that resemble the Gauss-Kronrod rule, provided that the integrand is analytic in a neighborhood of T.The work of B. de la Calle received support from Dirección General de Investigación (DGI), Ministerio de Educación y Ciencia, under grants MTM2006-13000-C03-02 and MTM2006-07186 and from UPM-CAM under grants CCG07-UPM/000-1652 and CCG07-UPM/ESP-1896. The work of G. López was supported by DGI under grant MTM2006-13000-C03-02 and by UC3M-CAM through CCG06-UC3M/ESP-0690. The work of L. Reichel was supported by an OBR Research Challenge Grant.Publicad

Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures

34 pages, no figures.-- MSC1991 codes: 42C05, 41A28.-- Dedicated to Barry Simon on the occasion of his sixtieth birthday.MR#: MR2220040 (2006m:42002)Zbl#: Zbl 1100.42014Let μ be a finite positive Borel measure with compact support consisting of an interval [c,d] ⊂ R plus a set of isolated points in R\[c,d], such that μ′>0 almost everywhere on [c,d]. Let $\{w_{2n}\}$, $n\in\Bbb Z_+$, be a sequence of polynomials, $\deg w_{2n}\leq2n$, with real coefficients whose zeros lie outside the smallest interval containing the support of μ. We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form $\frac{d\mu_n}{w_{2n}}$. In particular, we obtain an analogue for varying measures of Denisov's extension of Rakhmanov's theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above.Research of D.B. Rolanía was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under Grant BFM 2003-06335-C03-02. Research of de la Calle Ysern was supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under Grants BFM 2002-04315-C02-01 and BFM 2003-06335-C03-02. Research of G.L. Lagomasino was supported by Grants INTAS 03-516637, NATO PST.CLG.979738, and by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under Grant BFM 2003-06335-C03-02.Publicad