Modern context-aware applications no longer justify their decisions based only on their own information but on the decisions and information of other applications in a similar context.  Acquiring context information of other entities in an distributed system is difficult task when using the current content centric solutions such as DHTs.  This project aims to build a distributed index that provides storage for the so called Presentities solely based on the state of their context information.  Furthermore, the stored Presentities must be efficiently accessible even if only some information of their current context is available. To fulfill these requirements the PAST DHT was extended to support range queries and modified to use points on a space-filling curve as index values. The simulation of the system has shown very good accuracy rates, on average 99%, for range queries by maintaining a logarithmic relationship to the amount of required messages sent in the DHT.  Problems have emerged from the lack of load balancing implemented into the used DHT, but it is still the case that the proposed method of using space-filling curves to build a context centric decentralized index is both sufficient and effective. Keywords: context awareness, indexing, space-flling curves, Hilbert curve,Pastry, PAST

With the large number of spatial queries for spatial data objects changing with time in many applications, e.g., the location based services and geographic information systems, spatio-temporal databases have been developed to manipulate them in spatial or temporal databases. We focus on queries for stationary and moving objects in the spatial database in the present. However, there is no total ordering for the large volume and complicated objects which may change their geometries with time. A spatial access method based on the spatial index structure attempts to preserve the spatial proximity as much as possible. Then, the number of disk access which takes the response time is reduced during the query processing. Therefore, in this dissertation, based on the NA-tree, first, we propose the NA-tree join method over the stationary objects. Our NA-tree join simply uses the correlation table to directly obtain candidate leaf nodes based on two NA-trees which have non-empty overlaps. Moreover, our NA-tree join accesses objects once from those candidate leaf nodes and returns pairs of objects which have non-empty overlaps. Second, we propose the NABP method for the continuous range queries over the moving objects. Our NABP method uses the bit-patterns of regions in the NA-tree to check the relation between the range queries and moving objects. Our NABP method searches only one path in the NA-tree for the range query, instead of more than one path in the R*-tree-based method which has the overlapping problem. When the number of range queries increases with time, our NABP method incrementally updates the affected range queries by bit-patterns checking, instead of rebuilding the index like the cell-based method. From the experimental results, we have shown that our NABP method needs less time than the cell-based method for range queries update and less time than the R*-tree-based method for moving objects update. Based on the Hilbert curve with the good clustering property, we propose the ANHC method to answer the all-nearest-neighbors query by our ONHC method. Our ONHC method is used to answer the one-nearest-neighbor query over the stationary objects. We generate direction sequences to store the orientations of the query block in the Hilbert curve of different orders. By using quaternary numbers and direction sequences of the query block, we obtain the relative locations of the neighboring blocks and compute their quaternary numbers. Then, we directly access the neighboring blocks by their sequence numbers which is the transformation of the quaternary numbers from base four to ten. The nearest neighbor can be obtained by distance comparisons in these blocks. From the experimental results, we have shown that our ONHC and ANHC methods need less time than CCSF method for the one-nearest-neighbor query and the method based on R*-trees for the all-nearest-neighbors query, respectively.

The design of multi-dimensional access methods is difficult as compared to those of one-dimensional case because of no total ordering that preserves spatial locality. One way is to look for the total order that preserves spatial proximity at least to some extent. A space-filling curve is a continuous path which passes through every point in a space once so giving a one-to-one correspondence between the coordinates of the points and the 1D-sequence numbers of points on the curve. The Hilbert curve is a famous space filling curve, since it has been shown to have strong locality preserving properties; that is, it is the best space-filling curve in minimizing the number of clusters. Hence, it has been extensively used to maintain spatial locality of multidimensional data in a wide variety of applications. A window query is an important query operation in spatial (image) databases. Given a Hilbert curve, a window query reports its corresponding orders without the need to decode all the points inside this window into the corresponding Hilbert orders. Chung et al. have proposed an algorithm for decomposing a window into the corresponding Hilbert orders. However, the Hilbert curve requires that the region is of size 2^k x 2^k, where k∈N. The intuitive method such as Chung et al.¡¦s algorithm is to directly use Hilbert curves in the decomposed areas and then connect them. They must generate a sequence of the scanned quadrants additionally before encoding and decoding the Hilbert order of one pixel and scan this sequence one time while encoding and decoding one pixel. In this dissertation, on the design of methods for window queries on a Hilbert curve, we propose an efficient algorithm, named as Quad-Splitting, for decomposing a window into the corresponding Hilbert orders on a Hilbert curve without individual sorting and merging steps. The proposed algorithm does not perform individual sorting and merging steps which are needed in Chung et al.¡¦s algorithm. From our experimental results, we show that the Quad-Splitting algorithm outperforms Chung et al.¡¦s algorithm. On the design of the methods for generating the Hilbert curve of an arbitrary-sized image, we propose approximately even partition approach to generate a pseudo Hilbert curve of an arbitrary-sized image. From our experimental results, we show that our proposed pseudo Hilbert curve preserves the similar strong locality property to the Hilbert curve. On the design of the methods for coding Hilbert curve of an arbitrary-sized image, we propose encoding and decoding algorithms. From our experimental results, we show that our encoding and decoding algorithms outperform the Chung et al.¡¦s algorithms.

¡@¡@Due to wireless communication technologies, positioning technologies, and mobile computing develop quickly, mobile services are becoming practical and important on big spatiotemporal databases management. Mobile service users move only inside a spatial space, e:g: a country. They often issue the K Nearest Neighbor (kNN) query to obtain data objects reachable through the spatial database. The challenge problem of mobile services is how to efficiently answer the data objects which users interest to the corresponding mobile users. One type of kNN query problems is the order-sensitive moving kNN (order-sensitive MkNN) query problem. In the order-sensitive MkNN query problem, the query point is dynamic and unpredictable, the kNN answers should be responded in real time and sorted by the distance in the ascending order. Therefore, how to respond the kNN answers effectively, incrementally and correctly is an important issue. Nutanong et al: have proposed the V*-kNN algorithm to process the order-sensitive MkNN query. The V*-kNN algorithm uses their the V*-diagram algorithm to generate the safe region. It also uses the Incremental Rank Updates algorithm (IRU) to handle the events while the query point passing the bisectors or the boundary of the safe region. However, the V*-kNN algorithm uses the BF-kNN algorithm to retrieve NNs, which is non-incremental. This makes the search time increase while the density of the object increases. Moreover, they do not consider the situation that there are multiple objects at the same order, and the situation that there are multiple events happen in a single step. These situations may cause that the kNN answers are incorrect. Therefore, in this thesis, we propose the Hilbert curve-based kNN algorithm (HC-kNN) algorithm to process the ordersensitive MkNN query. The HC-kNN algorithm can handle the situation that there are multiple events happen in a single step. We also propose new data structure of the kNN answers. Next, we propose the Intersection of Perpendicular Bisectors algorithm (IPB) in order to handle order update events of the kNN answers. The IPB algorithm handles the situation which there are multiple objects at the same order. Finally, based on the Hilbert curve index, we propose the ONHC-kNN algorithm to get NNs incrementally and to generate the safe region. The safe region will not be affected while the density of the object increases. The safe region of our algorithm is larger than that of the V*-kNN algorithm. From our simulation result, we show that the HC-kNN algorithm provides better performance than the V*-kNN algorithm.

Les courbes remplissant l'espace sont connues pour la capacité d'ordonner les points multidimensionnels sur une ligne en tout conservant la localité, i.e. les points proches sont toujours proches sur la ligne. La conservation de la localité est beaucoup recherchée dans plusieurs applications. La courbe de Hilbert est la courbe remplissant l'espace qui conserve le mieux la localité. Cette courbe est originalement proposée en 2D, i.e. n'est qu'applicable aux points dans un espace 2D. Pour une perspective d'application dans le cas multidimensionnel, nous proposons dans cette thèse une généralisation de la courbe de Hilbert. La courbe généralisée est définie en s'appuyant sur la propriété essentielle de la courbe de Hilbert qui crée son niveau de conservation de la localité : l'adjacence. Ainsi, elle évite la dépendance du motif primitif RBG qui est le seul motif primitif de la courbe étendu par les recherches précédentes. Le résultat est donc une famille de courbe conservant bien la localité. L'optimisation de la conservation de la localité est aussi abordée pour permettre de retrouver la courbe qui conserve le mieux la localité. Pour cet objectif, nous proposons une mesure de la conservation de la localité. En s'appuyant sur les paramètres, cette mesure peut adapter aux différentes situations applicatives comme le changement de métrique ou de taille de localité. La construction est une partie importante de la thèse, elle est la base du calcul de l'index utilisé dans l'application. Pour un calcul de l'index rapide, la courbe de Hilbert autosimilaire est utilisée. La courbe de Hilbert satisfaisant les conditions de la courbe fait l'objet du chapitre 4. La courbe généralisée est enfin appliquée dans la recherche d'image. Il s'agit d'une recherche par le contenu où chaque image est caractérisée par un vecteur multidimensionnel. Les images sont ordonnées par la courbe sur une ligne ; ainsi, la recherche est simplifiée en une recherche sur une liste ordonnée. En donnant une image d'entrée, les images similaires sont celles correspondantes aux index voisins de l'index de l'image d'entrée. La conservation de la localité garantit que ces index correspondent aux images similaires. / The space-filling curves are known for the ability to order the multidimensional points on a line while preserving the locality, i.e. the close points are closely ordered on the line. The locality preserving is wished in many applications. Hilbert curve is the best locality preserving space-filling curve. This curve is originally proposed in 2D, i.e. it is only applied to points in a 2D space. For application in the multidimensional case, we propose in this thesis a generalization of Hilbert curve. Generalized curve is based on the essential property of Hilbert curve that creates its level of locality preserving: the adjacency. Thus, it avoids the dependence on the pattern RBG, which is the only pattern of the curve extended by previous researches. The result is a family of curves preserving well the locality. The optimization of the locality preserving is also addressed to find out the best locality preserving curve. For this purpose, we propose a measure of the locality preserving. Based on the parameters, this measure can adapt to different application situations such as the change of metric or locality size. The curve construction is an important part of the thesis. It is the basis of the index calculation used in application. For a rapid index calculation, the self-similar Hilbert curves is used. They are Hilbert curves satisfying the self-similar conditions specified in chapitre 4. The generalized curve is finally applied in image search. It is the question of the content-based image search (CBIR) where each image is characterized by a multidimensionalvector. Images are ordered by the curve of a line, and the search is simplified to the search on an ordered list. By giving an input image, similar images are those corresponding to neighbors of the index of the input. The locality preserving ensures that these indexes correspond to similar images.

In computational fluid dynamics, we often need to solve complex problems with high precision and efficiency. We propose a three-pronged approach to attain this goal. First, we use the discontinuous Galerkin spectral element method (DG-SEM) for its high accuracy. Second, we use graphics processing units (GPUs) to perform our computations to exploit available parallel computing power. Third, we implement a parallel adaptive mesh refinement (AMR) algorithm to efficiently use our computing power where it is most needed. We present a GPU DG-SEM solver with AMR and dynamic load balancing for the 2D wave equation. The DG-SEM is a higher-order method that splits a domain into elements and represents the solution within these elements as a truncated series of orthogonal polynomials. This approach combines the geometric flexibility of finite-element methods with the exponential convergence of spectral methods. GPUs provide a massively parallel architecture, achieving a higher throughput than traditional CPUs. They are relatively new as a platform in the scientific community, therefore most algorithms need to be adapted to that new architecture. We perform most of our computations in parallel on multiple GPUs. AMR selectively refines elements in the domain where the error is estimated to be higher than a prescribed tolerance, via two mechanisms: p-refinement increases the polynomial order within elements, and h-refinement splits elements into several smaller ones. This provides a higher accuracy in important flow regions and increases capabilities of modeling complex flows, while saving computing power in other parts of the domain. We use the mortar element method to retain the exponential convergence of high-order methods at the non-conforming interfaces created by AMR. We implement a parallel dynamic load balancing algorithm to even out the load imbalance caused by solving problems in parallel over multiple GPUs with AMR. We implement a space-filling curve-based repartitioning algorithm which ensures good locality and small interfaces. While the intense calculations of the high order approach suit the GPU architecture, programming of the highly dynamic adaptive algorithm on GPUs is the most challenging aspect of this work. The resulting solver is tested on up to 64 GPUs on HPC platforms, where it shows good strong and weak scaling characteristics. Several example problems of increasing complexity are performed, showing a reduction in computation time of up to 3× on GPUs vs CPUs, depending on the loading of the GPUs and other user-defined choices of parameters. AMR is shown to improve computation times by an order of magnitude or more.

This thesis focuses on range searching data structures, an elementary problem in computational geometry with research spanning decades. These problems often involve very large data sets. Processor speeds increase faster than memory speeds, thus the gap between the rate at which CPUs can process data and the rate at which it can be retrieved is increasing. To bridge this gap, various levels of cache are used. Since cache misses are costly, algorithms should be cache-friendly. The input-output (I/O) model was the first model for constructing cache-efficient algorithms, focusing on a two-level memory hierarchy. Algorithms for this model require manual tuning to determine optimal values for hardware dependent parameters, and are only optimal at a single level of a memory hierarchy. Cache-oblivious (CO) algorithms are built without knowledge of the hierarchy, allowing them to be optimal across all levels at once. There exist strong theoretical and practical results for I/O-efficient range searching. Recently, the CO model has received attention, but range searching remains poorly understood. This thesis explores data structures for CO range counting and reporting. It presents the first space and worst-case query-time optimal approximate range counting structure for a family of related problems, and associated O(N log N)-space query-optimal reporting structures. The approximate counting structure is the first of its kind in internal memory, I/O and CO models. Researchers have been trying to create linear-space query-optimal CO reporting structures. This thesis shows that for a variety of problems, linear space is in fact impossible. Heuristics are also used for building cache-friendly algorithms. Space-filling curves are continuous functions mapping multi-dimensional sets into one-dimensional ones. They are used to build search structures in the hopes that objects that were close in the original space remain close in the resulting ordering. This results in queries incurring fewer page swaps when traversing the structure. The Hilbert curve is notably good at this, but often imposes a space or time penalty. This thesis introduces compact Hilbert indices, which remove the ineffiency inherent for input point sets with bounding boxes smaller than their bounding hypercubes.

This Master's thesis deals with history of Fractal geometry and describes the fractal science development. In the begining there are essential Fractal science terms explained. Then description of fractal types and typical or most known examples of them are mentioned. Fractal knowledge application besides computer graphics area is discussed. Thesis informs about fractal geometry practical usage. Few present software packages or more programs which can be used for making fractal pictures are described in this work. Some of theirs capabilities are described. Thesis' practical part consists of slides, demonstrational program and poster. Electronical slides represents brief scheme usable for fractal geometry realm lectures. Program generates selected fractal types. Thesis results are projected on poster.