Extending a Spatial Database System by Graphs and Object Class Hierarchies

Two important open problems in spatial database systems are the modeling and implementation of spatially embedded networks and the handling of inhomogeneous collections of spatial objects. We sketch a data model that together with relations provides graphs as explicit structures. Graphs allow to model spatial networks; they consist of nodes, edges, and explicit paths. Inhomogeneous collections of objects can be represented in object type hierarchies which are in turn realized by tuple hierarchies. The resulting model contains the relational model; hence it is still possible to ask standard relational queries. At the implementation level, we describe a simple general purpose data structure for the representation of graphs on external storage. lt is shown how such a graph representation module can be embedded into the architecture of an extensible relational database system, the Gral system, and also how it can be implemented with relatively little effort in such an environment. Hence we obtain a strategy to migrate from a given relational system with spatial data types to a system with graphs and object class hierarchies

Integrating Programs and Documentation

A simple tool called PD system is described and offered for general use that allows one to integrate programs and their documentation in ASCII files. Such a program with documentation file (PD file) consists of alternating documentation and program sections. PD files can be compiled directly; for a compiler, documentation sections are just commentaries to be ignored. On the other hand, the PD system allows one to transform PD files into LaTeX source files and so to produce formatted documents. For the description of formatted material in the documentation sections, a simple markup language is offered. The main goal in the design of this language is readability of the source text. In other words, formatting specifications are kept as “implicit” and “invisible” as possible and much of the “formatting noise” occurring in LaTeX and other markup languages can be hidden. PD files should be readable for anyone without prior learning of the markup language

External Segment Trees

The segment tree is a well known internal data structure with numerous applications in computati.onal geometry. lt allows to maintain dynamically a set of intervals such that the intervals enclosing a query point can be found efficiently (point enclosure search). In this paper we transfer the underlying principle of the segment tree in a non-trivial way to secondary storage and arrive at the EST - an external file structure with the same functionality and the following properties: (1) Point enclosure searches are very efficient - only very few pages are accessed that are not filled to more than 50% with result intervals. (2) A page filling of 50% is guaranteed - on the average it will be around 70%. Although the segment tree represents in the worst case each interval by a logarithmic number of fragments, in practical cases fragmentation remains low and the storage requirements about linear. (3) The EST is balanced and the update algorithms are efficient. (4) Unlike many other file structures for spatial objects the EST has no problems with an arbitrary density, that is, an arbitrarily !arge number of intervals covering any point of the line. Furthermore, the EST can be used as a file structure constructor in the following sense: Let there be a file structure X supporting searches for objects with property x and suppose one needs to maintain a collection of objects with associated (e.g. time) intervals. Then one can build an EST-X structure that supports searches for objects with property x present at time t. This suggests to use the EST as a building block in the implementation of temporal database systems. Other applications include the one-dimensional indexing of collections of spatial objects in two or more dimensions. More generally, this paper shows techniques for mapping internal tree structures with node lists (other examples: range tree, interval tree) to secondary memory. In this context, an intriguing theoretical problem, the cover balancing problem, is solved: Given a tree whose nodes have associated weights partitioned into subtrees whose weights must lie in' a certain range, maintain this partition under weight changes at arbitrary nodes. This is in contrast to classical balancing problems where updates occur only at the leaves

XP-Trees: External Priority Search Trees

XP-trees (external priority search trees) are simple, practical and versatile structures supporting searches on points, intervals and higher dimensional spatial objects in secondary memory. Our approach to developing external structures is to consider worst-case efficient (internal) data structures from computational geometry, here the priority search tree. With the XP-tree we succeeded in transferring the underlying principle in an appropriate way to organize secondary storage, arriving at a practically useful structure. Together with external counterparts of other structures from computational geometry, such as segment tree, interval tree, and range tree, XP-trees can be used as building blocks to construct nested tree structures directly representing sets of spatial objects in higher dimensions. Like the internal counterpart, the XP-tree supports "halfrange" queries on points in two dimensions. Although XP-trees are not fully dynamic we believe them to be useful in many applications. Regarding balanced XP-trees, O(logdn + t) external accesses in halfrange queries are guaranteed, where n is the number of points, d the degree of the XP-tree, and t the number of points within a halfrange. Mapping intervals, as one-dimensional spatial objects, into two-dimensional points in the standard way, the structure supports all interesting kinds of queries on intervals. An XP-tree also supports queries on spatial objects in more dimensions by projecting them to an interval in one dimension. Hence the XP-tree can be used as an index structure in temporal or geometric databese systems. Experimentalperformance evaluations show that halfrange queries on two-dimensional point sets as well as all types of interval and point queries on sets of intervals are supported efficiently by the structure. Searching is quite fast, when no or few objects are retrieved. Although the shape of an XP-tree degenerates when a point set representation of a set of intervals is stored, the searching behaviour is practically the same as for a corresponding balanced structure. Searching is either very fast or has a large "retrieval ratio"

Rule-Based Optimzation and Query Processing in an Extensible Geometric Database System: (Revised Version July 1990)

Gral is an extensible database system based on the formal concept of a many-sorted relational algebra. Many-sorted algebra is used to define any application's query language, its query execution language, and its optimization rules. In this paper we describe Gral's optimization component. lt provides (1) a sophisticated rule language - rules are transformations of abstract algebra expressions, (2) a general optimization framework under which more specific optimization algorithms can be implemented, and (3) several control mechanisms for the application of rules. An optimization algorithm can be specified as a series of steps. Each step is defined by its own collection of rules together with a selected control strategy. The general facilities are illustrated by the complete design of an example optimizer - in the form of a rule file - for a small non-standard query language and an associated execution language. The query language includes selection, join, ordering, embedding derived values, aggregate functions, and several geometric operations. The example shows in particular how the special processing techniques of a geometric database system such as spatial join methods and geometric index structures can be integrated into query processing and optimization of a relational database system. A similar, though larger, optimizer is fully functional within the geometric database system implemented as a Gral prototype

Realm-Based Spatial Data Types: The ROSE Algebra

Spatial data types or algebras for database systems should (i) be fully general (which means, closed under set operations, hence e.g. a region value can be a set of polygons with holes), (ii) have formally defined semantics, (iii) be defined in terms of finite representations available in computers, (iv) offer facilities to enforce geometric consistency of related spatial objects, and (v) be independent of a particular DBMS data model, but cooperate with any. We offer such a definition. A central idea is to use realms as geometric domains underlying spatial data types. A realm as a general database concept is a finite, dynamic, user-defined structure underlying one or more system data types. A geometric realm defined here is a planar graph over a finite resolution grid. Problems of numerical robustness and topological correctness are solved below and within the realm layer so that spatial algebras defined above a realm enjoy very nice algebraic properties. Realms also interact with a DBMS to enforce geometric consistency on object creation or update. Tue ROSE algebra is defined on top of realms and offers general types to represent point, line, and region features together with a comprehensive set of operations. lt is described within a polymorphic type system and interacts with a DBMS data model and query language through an abstract object model interface. An example integration of ROSE into the object-oriented data model 0₂ and its query language is presented

BBoxDB: A Distributed and Highly Available Key-Bounding-Box-Value Store

BBoxDB is a distributed and highly available key-bounding-box-value store, which is designed to handle multi-dimensional big data. The software splits data into multi-dimensional shards and spreads them across a cluster of nodes. In contrast to existing key-value stores, BBoxDB stores each value together with an n-dimensional axis parallel bounding box. The bounding box describes the spatial location of the value in an n-dimensional space. A space partitioner (e.g., a K-D Tree, a Quad-Tree or a Grid) is used to split up the n-dimensional space into disjoint regions (distribution regions). Distribution regions are created dynamically, based on the stored data. BBoxDB can handle growing and shrinking datasets. The data redistribution is performed in the background and does not affect the availability of the system; read and write access is still possible at any time. Multi-dimensional data can be retrieved using hyperrectangle queries; these queries are efficiently supported by indices. Moreover, BBoxDB introduces distribution groups, the data of all tables of a distribution group are distributed in the same way (co-partitioned). Spatial-joins on co-partitioned tables can be executed efficiently without data shuffling between nodes. BBoxDB supports spatial-joins out-of-the-box using the bounding boxes of the stored data. Spatial-joins are supported by a spatial index and executed in a distributed and parallel manner on the nodes of the cluster

Explicit Graphs in a Functional Model for Spatial Databases

Observing that networks are ubiquitous in applications for spatial databases, we define a new data model and query language that especially supports graph structures. This model integrates concepts of functional data modeling with order-sorted algebra. Besides object and data type hierarchies graphs are available as an explicit modeling tool, and graph operations are part of the query language. Graphs have three classes of components, namely nodes, edges, and explicit paths. These are at the same time object types within the object type hierarchy and can be used like any other type. Explicit paths are useful because “real world” objects often correspond to paths in a network. Furthermore, a dynamic generalization concept is introduced to handle heterogeneous collections of objects in a query. In connection with spatial data types this leads to powerful modeling and querying capabilities for spatial databases, in particular for spatially embedded networks such as highways, rivers, public transport, and so forth. We use multi-level order-sorted algebra as a formal framework for the specification of our model. Roughly spoken, the first level algebra defines types and operations of the query language whereas the second level algebra defines kinds (collections of types) and type constructors as functions between kinds and so provides the types that can be used at the first level

Einblicke in "Genderism" im schulischen Verhalten

In dem Beitrag wird der Frage nachgegangen, wie Geschlecht in schulischen Interaktionen konstruiert wird. Entgegen der scheinbaren Selbstverständlichkeit, dass das Geschlecht natürlich und ohne gesellschaftliches Zutun vorhanden ist, wird in Auseinandersetzung mit den theoretischen Ansätzen von E. Goffman, E. West, D. H. Zimmerman und P. Bourdieu Geschlecht als eine sozial hergestellte Kategorie konzeptualisiert. Vor dem Hintergrund der unhintergehbaren Subjektivität von Forschung werden methodisch die Zugänge der Ethnographinnen im Forschungsprozess einerseits reflektierend expliziert und andererseits zu dem Versuch genutzt, Einblicke in sonst verdeckte Vorgänge der Konstruktion von Geschlecht zu erhalten. Anhand zweier Beispiele aus dem Deutschunterricht werden "Genderism" (Goffman) schulischen Verhaltens herausgearbeitet. Durch das Auseinanderfallen von übernommener Rolle und handelnder Person im Unterricht treten Irritationen mit der Geschlechtszugehörigkeit auf. Diese verweisen auf die interaktionelle Arbeit, die im Schulalltag notwendig ist, um Geschlecht stimmig darzustellen. (DIPF/Orig.)The authors inquire into the question of how gender is constructed through interaction at school. In Opposition to the apparent self-evidence that gender exists naturally and without societal assistance, they conceptualize gender as a socially produced category through the analysis of the theoretical approaches of Goffman, West/Zimmerman, and Bourdieu. The methods of examination of the ethnographers in the research process are presented against the background of the unavoidable subjectivity of research in two ways. On the one hand, they are explicated reflectively. On the other hand, they are used in the attempt to preserve insights into the otherwise hidden processes in the construction of gender. The authors develop the "Genderism" of school conduct using two examples from German instruction. In instruction, confusion with sexual orientation arises through the failing apart of the assumed role and the active person. This confusion points out the interactive work necessary in schools in order to represent gender coherently. (DIPF/Orig.

Spatio-Temporal Data Types: An Approach to Modeling and Querying Moving Objects in Databases

Spatio-temporal databases deal with geometries changing over time. In general, geometries cannot only change in discrete steps, but continuously, and we are talking about moving objects. If only the position in space of an object is relevant, then moving point is a basic abstraction; if also the extent is of interest, then the moving region abstraction captures moving as well as growing or shrinking regions. We propose a new line of research where moving points and moving regions are viewed as three-dimensional (2D space + time) or higher-dimensional entities whose structure and behavior is captured by modeling them as abstract data types. Such types can be integrated as base (attribute) data types into relational, object-oriented, or other DBMS data models; they can be implemented as data blades, cartridges, etc. for extensible DBMSs. We expect these spatio-temporal data types to play a similarly fundamental role for spatio-temporal databases as spatial data types have played for spatial databases. The paper explains the approach and discusses several fundamental issues and questions related to it that need to be clarified before delving into specific designs of spatiotemporal algebras