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Geometry and topology are both central concepts in geospatial data modelling and management. While geometry is the central concept for computational geometry applications, e.g. to intersect surfaces and solids in 3D space, topology is helpful for many application classes starting from city modelling to subsurface modelling and indoor navigation. Furthermore, p-adic numbers are useful for describing hierarchical processes on topological models. In this paper we first shortly review geometry- and topology-based approaches used for geospatial applications. We then describe our approach on turning geometry "upside down" focusing on topology during the whole process of distributed geospatial computing, data modelling, data management, and simulation. Furthermore, the way to use p-adic numbers for the description of hierarchical processes on topological models is shown for the example of simulation and the idea of p-adic analysis in distributed simulations is presented in the context of topological city and building models. The approach opens new insights such as topological relationships, components, and efficiently studying of the approximate behaviour of processes in the built environment using distributed computational systems. Finally, exemplary applications are presented to underline the importance of this new approach. [ABSTRACT FROM AUTHOR]

Despite the attention that direction relations, such as east, southeast etc., have attracted in several domains related to Spatial Databases and Geographic Information Systems (GIS), little work has been done on their formalization and efficient processing. In this paper we define direction relations between two-dimensional objects in different levels of qualitative resolution and we show how these relations can be efficiently retrieved in existing DBMSs using B- , KDB- and R- tree-based data structures. Since query processing involving direction relations maps into range queries in two- dimensional space, our work essentially studies optimization techniques for 2D ranges. We test the efficiency of alternative indexing methods through extensive experimentation and we present analytical models that estimate their performance. The analytical estimates are proved to be very close to the actual results and can be used by spatial query optimizers in order to decide the appropriate data structure for each type of range query. Although for our experiments we define a small set of representative relations motivated by geographic applications, the results of this paper are directly applicable to any type of direction relations (or range queries in general) that may arise in different application domains.

PageRank is a popular measure of centrality that is often applied to rank nodes in real-world networks. However, in many cases, the notion of teleportation is counterintuitive because it implies that whatever is moving around the network will jump or 'teleport' directly from one node to any other, without considering how far apart the nodes are. To overcome this issue, we propose here a general measure of PageRank centrality whereby the teleportation probabilities depend, in some way, on the distance separating the nodes. We accomplish this by drawing upon recent advances in non-local random walks, which allow the proposed measure to be tailored for various real-world networks and applications. To illustrate the flexibility of the proposed measure and to demonstrate how it differs from PageRank centrality, we present and discuss experimental results for a selection of real-world spatial and social networks, including an air transportation network, a collaboration network and an urban street network. [ABSTRACT FROM AUTHOR]

Large cartographic organizations worldwide produce generalized map series (GMS) in order to meet various user requirements. A GMS consists of maps of the same geographic region at different scales. Most of these maps currently are designed in a digital environment, and recently some of them have been distributed through the web. One important issue is the appropriate modeling and handling of cartographic entities composing individual maps in a GMS. Since these entities have rather complex descriptions and may be provided by various agencies, they usually do not conform to a fixed schema (i.e., they do not have a common structure). Hence, their representation in traditional data models, such as the relational or object-oriented, is not always feasible. This paper investigates the use of semi-structured data (SSD) models--an innovative approach recently developed in Information Technology for representing and handling entities in a GMS. Specifically, the Object Exchange Model (OEM), a popular database model for SSD, has been adopted to represent a GMS. How useful information can be extracted from such a representation using the LOREL query language--a popular language for SSD--is also shown. KEYWORDS: Map generalization, generalized map series (GMS), semi-structured data (SSD), Object Exchange Model (OEM), Lightweight Object REpository (LORE) system, LORE query Language (LOREL)., Introduction Information Technology (IT) scientists recently have focused their efforts on developing innovative methodologies for modeling and handling semi-structured data (SSD) in order to enhance the efficiency of software systems [...]

The foundation of modern Digital Earth frameworks is the Discrete Global Grid System (DGGS). To standardize the DGGS model, the Open Geospatial Consortium (OGC) recently created the DGGS Abstract Specification, which also aims to increase usability and interoperability between DGGSs. To support these demands and aid future research, open implementations are necessary. However, several OGC conformant DGGSs are not available for researchers to use. This has motivated us to develop an open-source web service that allows users to create quadrilateral grids based on the rHEALPix DGGS. In this paper, we describe the implementation of the web service, including issues and limitations, and demonstrate how discrete global grids and regional grids can be created. Lastly, we present examples that show how vector data sets can be modeled and integrated at different levels of resolution – a key benefit of the DGGS model. [ABSTRACT FROM AUTHOR]

Selection and join queries are fundamental operations in Data Base Management Systems (DBMS). Support for nontraditional data, including spatial objects, in an efficient manner is of ongoing interest in database research. Toward this goal, access methods and cost models for spatial queries are necessary tools for spatial query processing and optimization. In this paper, we present analytical models that estimate the cost (in terms of node and disk accesses) of selection and join queries using R-tree-based structures. The proposed formulae need no knowledge of the underlying R-tree structure(s) and are applicable to uniform-like and nonuniform data distributions. In addition, experimental results are presented which show the accuracy of the analytical estimations when compared to actual runs on both synthetic and real data sets. Index Terms--Spatial databases, access methods, query optimization, cost models, R-trees.