Multi-Step Processing of Spatial Joins

Spatial joins are one of the most important operations for combining spatial objects of several relations. In this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by the following two steps. First of all, sophisticated approximations are used to identify answers as well as to filter out false hits from the set of candidates. For this purpose, we investigate various types of conservative and progressive approximations. In the last step, the exact geometry of the remaining candidates has to be tested against the join predicate. The time required for computing spatial join predicates can essentially be reduced when objects are adequately organized in main memory. In our approach, objects are first decomposed into simple components which are exclusively organized by a main-memory resident spatial data structure. Overall, we present a complete approach of spatial join processing on complex spatial objects. The performance of the individual steps of our approach is evaluated with data sets from real cartographic applications. The results show that our approach reduces the total execution time of the spatial join by factors

Computable decision making on the reals and other spaces via partiality and nondeterminism

Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause errors and jeopardize safety. Some programming systems implement exact real arithmetic, which resolves this matter but complicates others, such as decision making. In these systems, it is impossible to compute (total and deterministic) discrete decisions based on connected spaces such as $\mathbb{R}$. We present programming-language semantics based on constructive topology with variants allowing nondeterminism and/or partiality. Either nondeterminism or partiality suffices to allow computable decision making on connected spaces such as $\mathbb{R}$. We then introduce pattern matching on spaces, a language construct for creating programs on spaces, generalizing pattern matching in functional programming, where patterns need not represent decidable predicates and also may overlap or be inexhaustive, giving rise to nondeterminism or partiality, respectively. Nondeterminism and/or partiality also yield formal logics for constructing approximate decision procedures. We implemented these constructs in the Marshall language for exact real arithmetic.Comment: This is an extended version of a paper due to appear in the proceedings of the ACM/IEEE Symposium on Logic in Computer Science (LICS) in July 201

Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating factor in CAD/CAM applications has necessitated the development of database systems with appropriate modelling and retrieval capabilities. One essential problem is the treatment of geometric data which has led to the development of spatial databases. Unfortunately, most proposals only deal with simple geometric objects like multidimensional points and rectangles. On the other hand, there has been a rapid development in the field of representing geometric objects with free form curves or surfaces, initiated by engineering applications such as mechanical engineering, aviation or astronautics. Therefore, we propose a concept for the realization of spatial retrieval operations on geometric objects with free form boundaries, such as B-spline or Bezier curves, which can easily be integrated in a database management system. The key concept is the encapsulation of geometric operations in a so-called query processor. First, this enables the definition of an interface allowing the integration into the data model and the definition of the query language of a database system for complex objects. Second, the approach allows the use of an arbitrary representation of the geometric objects. After a short description of the query processor, we propose some representations for free form objects determined by B-spline or Bezier curves. The goal of efficient query processing in a database environment is achieved using a combination of decomposition techniques and spatial access methods. Finally, we present some experimental results indicating that the performance of decomposition techniques is clearly superior to traditional query processing strategies for geometric objects with free form boundaries

Leveraging range joins for the computation of overlap joins

Joins are essential and potentially expensive operations in database management systems. When data is associated with time periods, joins commonly include predicates that require pairs of argument tuples to overlap in order to qualify for the result. Our goal is to enable built-in systems support for such joins. In particular, we present an approach where overlap joins are formulated as unions of range joins, which are more general purpose joins compared to overlap joins, i.e., are useful in their own right, and are supported well by B+-trees. The approach is sufficiently flexible that it also supports joins with additional equality predicates, as well as open, closed, and half-open time periods over discrete and continuous domains, thus offering both generality and simplicity, which is important in a system setting. We provide both a stand-alone solution that performs on par with the state-of-the-art and a DBMS embedded solution that is able to exploit standard indexing and clearly outperforms existing DBMS solutions that depend on specialized indexing techniques. We offer both analytical and empirical evaluations of the proposals. The empirical study includes comparisons with pertinent existing proposals and offers detailed insight into the performance characteristics of the proposals

The impact of spatial data redundancy on SOLAP query performance

Geographic Data Warehouses (GDW) are one of the main technologies used in decision-making processes and spatial analysis, and the literature proposes several conceptual and logical data models for GDW. However, little effort has been focused on studying how spatial data redundancy affects SOLAP (Spatial On-Line Analytical Processing) query performance over GDW. In this paper, we investigate this issue. Firstly, we compare redundant and non-redundant GDW schemas and conclude that redundancy is related to high performance losses. We also analyze the issue of indexing, aiming at improving SOLAP query performance on a redundant GDW. Comparisons of the SB-index approach, the star-join aided by R-tree and the star-join aided by GiST indicate that the SB-index significantly improves the elapsed time in query processing from 25% up to 99% with regard to SOLAP queries defined over the spatial predicates of intersection, enclosure and containment and applied to roll-up and drill-down operations. We also investigate the impact of the increase in data volume on the performance. The increase did not impair the performance of the SB-index, which highly improved the elapsed time in query processing. Performance tests also show that the SB-index is far more compact than the star-join, requiring only a small fraction of at most 0.20% of the volume. Moreover, we propose a specific enhancement of the SB-index to deal with spatial data redundancy. This enhancement improved performance from 80 to 91% for redundant GDW schemas.FAPESPCNPqCoordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)INEPFINE

Distributed Evaluation of Top-k Temporal Joins

To appear in SIGMOD'16We study a particular kind of join, coined Ranked Temporal Join (RTJ), featuring predicates that compare time intervals and a scoring function associated with each predicate to quantify how well it is satisfied. RTJ queries are prevalent in a variety of applications such as network traffic monitoring , task scheduling, and tweet analysis. RTJ queries are often best interpreted as top-k queries where only the best matches are returned. We show how to exploit the nature of temporal predicates and the properties of their associated scoring semantics to design TKIJ , an efficient query evaluation approach on a distributed Map-Reduce architecture. TKIJ relies on an offline statistics computation that, given a time partitioning into granules, computes the distribution of intervals' endpoints in each granule, and an online computation that generates query-dependent score bounds. Those statistics are used for workload assignment to reducers. This aims at reducing data replication, to limit I/O cost. Additionally , high-scoring results are distributed evenly to enable each reducer to prune unnecessary results. Our extensive experiments on synthetic and real datasets show that TKIJ outperforms state-of-the-art competitors and provides very good performance for n-ary RTJ queries on temporal data

Geographica: A Benchmark for Geospatial RDF Stores

Geospatial extensions of SPARQL like GeoSPARQL and stSPARQL have recently been defined and corresponding geospatial RDF stores have been implemented. However, there is no widely used benchmark for evaluating geospatial RDF stores which takes into account recent advances to the state of the art in this area. In this paper, we develop a benchmark, called Geographica, which uses both real-world and synthetic data to test the offered functionality and the performance of some prominent geospatial RDF stores

Efficient processing of large-scale spatio-temporal data

Millionen Geräte, wie z.B. Mobiltelefone, Autos und Umweltsensoren senden ihre Positionen zusammen mit einem Zeitstempel und weiteren Nutzdaten an einen Server zu verschiedenen Analysezwecken. Die Positionsinformationen und übertragenen Ereignisinformationen werden als Punkte oder Polygone dargestellt. Eine weitere Art räumlicher Daten sind Rasterdaten, die zum Beispiel von Kameras und Sensoren produziert werden. Diese großen räumlich-zeitlichen Datenmengen können nur auf skalierbaren Plattformen wie Hadoop und Apache Spark verarbeitet werden, die jedoch z.B. die Nachbarschaftsinformation nicht ausnutzen können - was die Ausführung bestimmter Anfragen praktisch unmöglich macht. Die wiederholten Ausführungen der Analyseprogramme während ihrer Entwicklung und durch verschiedene Nutzer resultieren in langen Ausführungszeiten und hohen Kosten für gemietete Ressourcen, die durch die Wiederverwendung von Zwischenergebnissen reduziert werden können. Diese Arbeit beschäftigt sich mit den beiden oben beschriebenen Herausforderungen. Wir präsentieren zunächst das STARK Framework für die Verarbeitung räumlich-zeitlicher Vektor- und Rasterdaten in Apache Spark. Wir identifizieren verschiedene Algorithmen für Operatoren und analysieren, wie diese von den Eigenschaften der zugrundeliegenden Plattform profitieren können. Weiterhin wird untersucht, wie Indexe in der verteilten und parallelen Umgebung realisiert werden können. Außerdem vergleichen wir Partitionierungsmethoden, die unterschiedlich gut mit ungleichmäßiger Datenverteilung und der Größe der Datenmenge umgehen können und präsentieren einen Ansatz um die auf Operatorebene zu verarbeitende Datenmenge frühzeitig zu reduzieren. Um die Ausführungszeit von Programmen zu verkürzen, stellen wir einen Ansatz zur transparenten Materialisierung von Zwischenergebnissen vor. Dieser Ansatz benutzt ein Entscheidungsmodell, welches auf den tatsächlichen Operatorkosten basiert. In der Evaluierung vergleichen wir die verschiedenen Implementierungs- sowie Konfigurationsmöglichkeiten in STARK und identifizieren Szenarien wann Partitionierung und Indexierung eingesetzt werden sollten. Außerdem vergleichen wir STARK mit verwandten Systemen. Im zweiten Teil der Evaluierung zeigen wir, dass die transparente Wiederverwendung der materialisierten Zwischenergebnisse die Ausführungszeit der Programme signifikant verringern kann.Millions of location-aware devices, such as mobile phones, cars, and environmental sensors constantly report their positions often in combination with a timestamp to a server for different kinds of analyses. While the location information of the devices and reported events is represented as points and polygons, raster data is another type of spatial data, which is for example produced by cameras and sensors. This Big spatio-temporal Data needs to be processed on scalable platforms, such as Hadoop and Apache Spark, which, however, are unaware of, e.g., spatial neighborhood, what makes them practically impossible to use for this kind of data. The repeated executions of the programs during development and by different users result in long execution times and potentially high costs in rented clusters, which can be reduced by reusing commonly computed intermediate results. Within this thesis, we tackle the two challenges described above. First, we present the STARK framework for processing spatio-temporal vector and raster data on the Apache Spark stack. For operators, we identify several possible algorithms and study how they can benefit from the underlying platform's properties. We further investigate how indexes can be realized in the distributed and parallel architecture of Big Data processing engines and compare methods for data partitioning, which perform differently well with respect to data skew and data set size. Furthermore, an approach to reduce the amount of data to process at operator level is presented. In order to reduce the execution times, we introduce an approach to transparently recycle intermediate results of dataflow programs, based on operator costs. To compute the costs, we instrument the programs with profiling code to gather the execution time and result size of the operators. In the evaluation, we first compare the various implementation and configuration possibilities in STARK and identify scenarios when and how partitioning and indexing should be applied. We further compare STARK to related systems and show that we can achieve significantly better execution times, not only when exploiting existing partitioning information. In the second part of the evaluation, we show that with the transparent cost-based materialization and recycling of intermediate results, the execution times of programs can be reduced significantly