A storage and access architecture for efficient query processing in spatial database systems

Due to the high complexity of objects and queries and also due to extremely large data volumes, geographic database systems impose stringent requirements on their storage and access architecture with respect to efficient query processing. Performance improving concepts such as spatial storage and access structures, approximations, object decompositions and multi-phase query processing have been suggested and analyzed as single building blocks. In this paper, we describe a storage and access architecture which is composed from the above building blocks in a modular fashion. Additionally, we incorporate into our architecture a new ingredient, the scene organization, for efficiently supporting set-oriented access of large-area region queries. An experimental performance comparison demonstrates that the concept of scene organization leads to considerable performance improvements for large-area region queries by a factor of up to 150

Query processing of spatial objects: Complexity versus Redundancy

The management of complex spatial objects in applications, such as geography and cartography, imposes stringent new requirements on spatial database systems, in particular on efficient query processing. As shown before, the performance of spatial query processing can be improved by decomposing complex spatial objects into simple components. Up to now, only decomposition techniques generating a linear number of very simple components, e.g. triangles or trapezoids, have been considered. In this paper, we will investigate the natural trade-off between the complexity of the components and the redundancy, i.e. the number of components, with respect to its effect on efficient query processing. In particular, we present two new decomposition methods generating a better balance between the complexity and the number of components than previously known techniques. We compare these new decomposition methods to the traditional undecomposed representation as well as to the well-known decomposition into convex polygons with respect to their performance in spatial query processing. This comparison points out that for a wide range of query selectivity the new decomposition techniques clearly outperform both the undecomposed representation and the convex decomposition method. More important than the absolute gain in performance by a factor of up to an order of magnitude is the robust performance of our new decomposition techniques over the whole range of query selectivity

A tetrahedral space-filling curve for non-conforming adaptive meshes

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neighbors of a mesh element in constant time, as well as the next and previous element in the space-filling curve and whether a given element is on the boundary of the root simplex or not. Our presentation concludes with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.Comment: 33 pages, 12 figures, 8 table

Vers un système de projection icosaédral hiérarchique global sans distorsions pour cartographie Web

Les systèmes de projection cartographique adaptés aux services de cartographie web, suscitent encore de nombreuses questions de recherche. La majorité des services de cartographie Web (ex. Google Maps, Bing Maps) utilise la Projection Web Mercator(WMP), mais cette dernière présente de grandes distorsions systématiques notamment dans les régions nordiques. Il nous est alors paru nécessaire de développer une autre méthode permettant de projeter la surface du globe avec un minimum de distorsion. Notre approche s’inspire de la projection myriahedrale qui suppose que chaque face du myriahedron est suffisamment petite de telle sorte que les distorsions soient négligeables. La méthode proposée consiste à explorer une nouvelle approche de tessellation de la surface du globe et qui permet de projeter la surface du globe sur les faces de la tessellation et à plusieurs niveaux de détails. Cela permet de compenser la faiblesse des méthodes de tessellations existantes utilisées dans la cartographie Web. Cette tessellation utilise un icosaèdre comme modèle géométrique de base avec une densité de partitionnement des faces de l’icosaèdre entre les niveaux de récursivité égale à 4.La méthodologie proposée consiste en quatre étapes successives: a) la construction d'une structure hiérarchique qui résulte de la subdivision récursive des faces de l'icosaèdre ; b) la définition d’un système de projection approprié à la tessellation icosaédrique; c) la projection des données géospatiales de la sphère terrestre sur chaque face de l’icosaèdre; d) le dépliage de la tessellation icosaédrique résultante sur un plan en utilisant des algorithmes de calcul du plus court chemin afin de maintenir le voisinage autour du point d’intérêt. Nous présenterons les étapes de développement et d’implémentation du système proposé et les résultats obtenus dans le cadre de ce projet de recherche. L’étude comparative avec d’autres systèmes de projection montre que notre approche minimise mieux les déformations par tout sur le globe et surtout dans les régions nordiques.Map projection systems adapted to web mapping services still raise many research questions. The majority of web mapping services (ex. Google Maps, Bing Maps) use Web Mercator Projection (WMP) which introduces large systematic distorsionsin spatial data especially in polar rigions. Therefore, it is necessary to develop an alternative method for projecting these regions with minimal distortions. Our approach is inspired of myriahedral projections which assume that each face of a myriahedron is small enough so that the distortions are negligible. Here, in this research work we propose a new approach for the tessellation of the surface of the globe and the projectionof the spatial information from the glob to the faces of the tessellation at differentlevels of details. This compensates for the weakness of the methods used for tessellation in the existing web mapping systems. The proposed tessellation is created based on an icosahedron with a partitioning density of the faces equal to 4. The proposed methodology consists of four stages: a) constructing of a hierarchical structure resulting the recursive subdivision of the faces of the icosahedron, while maintaining topological relationships between the triangles in each level of detail; b) defining of an appropriate projection system to the icosahedral tessellation; c) projecting of geospatial data of the terrestrial sphere on each face of the icosahedron; d) unfolding the resulting icosahedral tessellation on a plane around a point of interest. Here we present different stages of development and implementation of the proposed system and the results obtained in the framework of this research project. The comparative study with other projection systems shows that our approach allows to better minimize different distortions every where on the globe and specially in the polar rigions

Scalable Algorithms for Parallel Tree-based Adaptive Mesh Refinement with General Element Types

In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used element type, such as for example lines, triangles, tetrahedra, quadrilaterals, hexahedra, and prisms. For triangular and tetrahedral elements (simplices) with red-refinement (1:4 in 2D, 1:8 in 3D), we develop a new SFC, the tetrahedral Morton space-filling curve (TM-SFC). Its construction is similar to the Morton index for quadrilaterals/hexa- hedra, as it is also based on bitwise interleaving the coordinates of a certain vertex of the simplex, the anchor node. Additionally, we interleave with a new piece of information, the so called type. For these simplices, we develop element local algorithms such as constructing the parent, children, or face-neighbors of a simplex, and show that most of them are constant-time operations independent of the refinement level. With SFC based partitioning it is possible that the mesh elements that are parti- tioned to one process do not form a face-connected domain. We prove the following upper bounds for the number of face-connected components of segments of the TM-SFC: With a maximum refine- ment level of L, the number of face-connected components is bounded by 2(L − 1) in 2D and 2L + 1 in 3D. Additionally, we perform a numerical investigation of the distribution of lengths of SFC segments. Furthermore, we develop a new approach to partition and repartition a coarse (input) mesh among the processes. Compared to previous methods it optimizes for fine mesh load-balance and reduces the parallel communication of coarse mesh data. We discuss the coarse mesh repartitioning algorithm and demonstrate that our method repartitions a coarse mesh of 371e9 trees on 917,504 processes (405,000 trees per process) on the Juqueen supercomputer in 1.2 seconds. We develop an AMR concept that works independently of the element type; achieving this independence by strictly distinguishing between functions that oper- ate on the whole mesh (high-level) and functions that locally operate on a single element or a small set of elements (low-level). We discuss a new approach to generate and manage ghost elements that fits into our element-type independent approach. We define and describe the necessary low-level algorithms. Our main idea is the computation of tree-to-tree face-neighbors of an element via the explicit construction of the element's face as a lower dimensional element. In order to optimize the runtime of this method we enhance the algorithm with a top-down search method from Isaac, Burstedde, Wilcox, and Ghattas, and demonstrate how it speeds up the computation by factors of 10 to 20 achieving runtimes comparable to state-of-the art implementations with fixed element types. With the ghost algorithm we build a straight-forward ripple version of the 2:1 balance algorithm. This is not an optimized version but it serves as a feasibility study for our element-type independent approach. We implement all algorithms that we develop in this thesis in the new AMR library t8code. Our modular approach allows us to reuse existing software, which we demonstrate by using the library p4est for quadrilateral and hexahedral elements. In a concurrent Bachelor's thesis by David Knapp (INS, Bonn) the necessary low-level algorithms for prisms were developed. With t8code we demonstrate that we can create, adapt, (re-)partition, and balance meshes, as well as create and manage a ghost layer. In various tests we show excellent strong and weak scaling behavior of our algorithms on up to 917,504 parallel processes on the Juqueen and Mira supercomputers using up to 858e9 mesh elements. We conclude this thesis by demonstrating how an application can be coupled with the AMR routines. We implement a finite volume based advection solver using t8code and show applications with triangular, quadrilateral, tetrahedral, and hexahedral elements, as well as 2D and 3D hybrid meshes, the latter consisting of tetrahedra, hexahedra, and prisms. Overall, we develop and demonstrate a new simplicial SFC and create a fast and scalable tree-based AMR software that offers a flexibility and generality that was previously not available

Développement d'une grille hexagonale hiérarchique et d'algorithmes de clustering "géosémantique" pour l'analyse et la découverte de connaissances géo-spatiales

Dans le cadre du projet MUSCAMAGSJ ± Multi-scale multi-agent geo-simulation ¿, les simulations sont produites dans un environnement virtuel géographique (EV G) qui reflète la réalité géographique grâce à l'usage de données géoréférencées. Compte tenu des applications de mobilité urbaine visées dans ce projet et de la disponibilité des données, l'EVG a été représenté par une grille hexagonale. Cependant, bien qu' il réduise le biais directionnel lors de l'analyse spatiale, ce genre de grille présente un inconvénient important: il ne permet pas une représentation multi -échelle de l'environnement géographique. Dans le cadre de ce projet de maîtrise, nous proposons une autre solution à ce problème. En effet, nous proposons de partitionner l'environnement à l'aide de cellules dont la forme géométrique fondamentale est le triangle équilatéral. Ensuite, à partir de ces cellules, nous développons un algorithme pour créer des cellules hexagonales hiérarchiques selon un indexage conforme à l'approche column-ordering. Ensuite nous intégrons ces grilles dans une application de système d'information géographique que nous emichissons par des techniques d'intelligence artificielle afin de faciliter la découverte et l'interprétation des phénomènes urbains. En effet, nous avons considéré plus particulièrement les automates cellulaires et les techniques de clustering issues du data mining. Ainsi, nous avons exploré une technique de regroupement ±géo-sémantique¿ des cellules en nous basant sur un algorithme de clustering par fusion. Également, nous avons associé aux grilles hexagonales hiérarchiques des automates cellulaires afin d'obtenir un processus de regroupement automatique (auto-regroupement) qui puisse être utilisé pour l'analyse des données spatiales

Développement d’une méthode d’automate cellulaire basé sur une tessellation irrégulière et hiérarchique pour la simulation des processus spatiotemporels

Les systèmes d’information géographique (SIG) sont largement utilisés pour représenter, gérer et analyser les données spatiales dans plusieurs disciplines incluant les géosciences, l’agriculture, la foresterie, la météorologie et l’océanographie. Néanmoins, malgré l’avancement récent des technologies des SIG, ils sont encore limités dans la représentation et la simulation des processus spatiotemporels. Ce travail de recherche définit le cadre théorique, conceptuel et applicatif qui vise à améliorer les méthodes de compréhension, de représentation et de simulation des processus dynamiques continus. Il vise plus précisément à améliorer les structures de données dans les SIG en développant une structure de données hiérarchique qui est la base d’un automate cellulaire capable de répondre aux principales caractéristiques de ces processus. L’exploration du potentiel des automates cellulaires pour simuler et représenter les processus dynamiques continus dans les SIG en respectant leur caractère irrégulier et hiérarchique fait l’objet de ce travail de recherche dans lequel une application dans le contexte hydrologique est mise en place. Nos objectifs spécifiques se résument dans 1) la construction d’une tessellation irrégulière et hiérarchique permettant de représenter les processus spatiotemporels et 2) la simulation de ces processus en utilisant un automate cellulaire opérant sur cette tessellation. Nous étudions la discrétisation de l’espace en tessellation irrégulière basée sur le diagramme de Voronoï et nous proposons une procédure de hiérarchisation de cette tessellation dans un objectif de représentation multi-échelle afin d’offrir une solution d’aide à la décision dans la gestion du territoire. Nous expliquons notre méthodologie et les algorithmes de sélection de données pour la génération de différents niveaux d’échelles spatiales. Un automate cellulaire non traditionnel est mis en place pour lequel nous définissons une grille à géométrie irrégulière de type Voronoï, des règles de transition spécifiques et un type particulier de voisinage orienté. Nous validons le fonctionnement de ce prototype dans le Bassin Expérimental de la Forêt Montmorency à Québec où des comparaisons sont possibles grâce à des données de débits d’eau mesurées in situ.Geographic information systems (GIS) are widely used to represent, manage and analyse spatial data in many disciplines including geosciences, agriculture, forestry, meteorology and oceanography. However, despite recent advances in GIS technologies, they are still limited when it comes to representation and simulation of spatiotemporal processes. This research work, deals with a theoretical, conceptual and practical framework which aims to improve the representation of dynamic continuous processes. It aims especially to improve GIS capabilities by developing a CA based on a hierarchical irregular tessellation which is able to take into account the main characteristics of these processes. The exploration of the cellular automata potential to simulate and represent dynamic continuous processes regarding their irregular and hierarchic characteristics is the subject of this work where an application in the hydrologic field is established. Our specific objectives are 1) to build an irregular and hierarchic grid that can be used to represent spatiotemporal processes, 2) to simulate those processes with a cellular automata operating on this grid. We give details about the irregular geometric grid based on a Voronoï Diagram, the characteristics of a specific oriented neighbourhood and the transition rules that are governing the cells update. In addition, we discuss the hierarchical perspective of the build lattice that is essential for easy move between different spatial scales. We explain our methodology of data selection in order to generate the spatial levels of representation by demonstrating the used selection algorithms. This facilitates the representation of spatial dynamic phenomena and contributes to the better understanding of the complex behaviour of the whole system at different levels of details. We also present the data structures and general functioning of the whole simulation system. We finally, validate our framework by simulating the water flow process in a specific watershed in the region of Montmorency Forest of Quebec where in situ data are available. To validate our simulation results we compare them with measured data