Distance Oracle on Terrain Surface

Due to the advancement of geo-positioning technology, the terrain data has become increasingly popular and has drawn a lot of research effort from both academia and industry. The distance computation on the terrain surface is a fundamental and important problem that is widely applied in geographical information systems and 3D modeling. As could be observed from the existing studies, online computation of the distance on the terrain surface is very expensive. All existing index-based methods are only efficient under the case where the distance query must be performed among a small set of predefined points-of-interest known apriori. But, in general cases, they could not scale up to sizable datasets due to their intolerable oracle building time and space consumption. In this paper, we studied the arbitrary point-to-arbitrary point distance query on the terrain surface in which no assumption is imposed on the query points, and the distance query could be performed between any two arbitrary points. We propose an indexing structure, namely Efficient Arbitrary Point-to-Arbitrary Point Distance Oracle (EAR-Oracle), with theoretical guarantee on the accuracy, oracle building time, oracle size and query time. Our experiments demonstrate that our oracle enjoys excellent scalability and it scales up to enormous terrain surfaces but none of the existing index-based methods could be able to. Besides, it significantly outperforms all existing online computation methods by orders of magnitude in terms of the query time.

Given a geometric graph in d-dimensional space, it is useful to preprocess it so that distance queries, exact or approximate, can be answered efficiently. Algorithms that can report distance queries in constant time are also referred to as “distance oracles”. With unlimited preprocessing time and space, it is clear that exact distance oracles can be easily designed. This entry sheds light on the design of approximate distance oracles with limited preprocessing time and space for the family of geometric graphs with constant dilation.

Energy-efficient air-indices for shortest path and distance queries on road networks

In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann (STOC 2019) showed that exact distance queries on planar graphs could be answered in $n^{o(1)}$ time by a data structure occupying $n^{1+o(1)}$ space, i.e., up to $o(1)$ terms, optimal exponents in time (0) and space (1) can be achieved simultaneously. Their distance query algorithm is recursive: it makes successive calls to a point-location algorithm for planar Voronoi diagrams, which involves many recursive distance queries. The depth of this recursion is non-constant and the branching factor logarithmic, leading to $(\log n)^{\omega(1)} = n^{o(1)}$ query times. In this paper we present a new way to do point-location in planar Voronoi diagrams, which leads to a new exact distance oracle. At the two extremes of our space-time tradeoff curve we can achieve either $n^{1+o(1)}$ space and $\log^{2+o(1)}n$ query time, or $n\log^{2+o(1)}n$ space and $n^{o(1)}$ query time. All previous oracles with $\tilde{O}(1)$ query time occupy space $n^{1+\Omega(1)}$, and all previous oracles with space $\tilde{O}(n)$ answer queries in $n^{\Omega(1)}$ time.

We present new distance computation algorithms using hierarchies of rectangular swept spheres. Each bounding volume of the tree is described as the Minkowski sum of a rectangle and a sphere, and fits tightly to the underlying geometry. We present accurate and efficient algorithms to build the hierarchies and perform distance queries between the bounding volumes. We also present traversal techniques for accelerating distance queries using coherence and priority directed search. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have achieved significant speedups on many benchmarks.

Multi-dimensional data structures are applied in many real index applications, i.e. data mining, indexing multimedia data, indexing of text documents and so on. Many index structures and algorithms have been proposed. There are two major approaches to multi-dimensional indexing: data structures to indexing metric and vector spaces. R-trees, R*-trees and (B)UB-trees are representatives of the vector data structures. These data structures provide efficient processing of many types of queries, i.e. point queries, range queries and so on. As far as the vector data structures are concerned, the range query retrieves all points in defined hyper box in an n-dimensional space. The narrow range query is an important type of the range query. Its processing is inefficient in vector data structures. Moreover, the efficiency decreases as the dimension of the indexed space increases. We depict an application of the signature for more efficient processing of narrow range queries. The approach puts the signature into the multi-dimensional data structures like R-tree or UB-tree but original functionalities are preserved, i.e. the range query algorithm for general range query. The novel data structure is called the signature data structure, e.g., Signature R-tree or Signature UB-tree.

For the performance of geographic information systems, it has been widely recognized that efficient data structures and algorithms supporting proximity based access to spatial data are a crucial ingredient. Because of that, in the last years, a lot of data structures for storage of multidimensional non-point objects have been proposed in the literature (for an overview see our tutorial introduction in this volume). Almost all of these approaches are made to support queries based on spatial neighborhood of objects, so-called proximity queries. Common examples of such proximity queries are range queries, returning all objects intersecting a given (rectangular) region, or nearest neighbor queries, determining the object nearest to a given point. But a geographic or cartographic information system should also support queries that do not exclusively refer to the spatial neighborhood of objects. For example, different versions of spatial data must be organized such that proximity queries to any version of the data can be answered efficiently. Or, given a set of object classes, a spatial query that involves an arbitrary combination of these classes should also be supported. Because of the growing size of data sets to be handled in geographic information systems, an appropriate data organisation to support such and several other application-specific queries becomes more and more important. In this paper, we will present two approaches for access structures supporting the two types of queries mentioned above. Handling of versioned, spatial data is the topic of Section 2, while Section 3 discusses queries on some classes selected from the set of object classes stored in a geographic information system.

In the past decades, shortest distance methods for road networks have been developed that focus on how to speed up the latency of a single source-target pair distance query. Large analytical applications on road networks including simulations (e.g., evacuation planning), logistics, and transportation planning require methods that provide high throughput (i.e., distance computations per second) and the ability to "scale out" by using large distributed computing clusters. A framework called SPDO is presented which implements an extremely fast distributed algorithm for computing road network distance queries on Apache Spark. The approach extends our previous work of developing the ε-distance oracle which has now been adapted to use Spark's resilient distributed dataset (RDD). Compared with state-of-the-art methods that focus on reducing latency, the proposed framework improves the throughput by at least an order of magnitude, which makes the approach suitable for applications that need to compute thousands to millions of network distances per second.

Emerging multimedia applications require database systems to provide support for new types of objects and to process queries that may have no parallel in traditional database applications. One such important class of queries are the proximity queries that aims to retrieve objects in the database that are related by a distance metric in a way that is specified by the query. The importance of proximity queries has earlier been realized in developing constructs for visual languages. In this paper, we present algorithms for answering a class of proximity queries-fixed-radius nearest-neighbor queries over point object. Processing proximity queries using existing query processing techniques results in high CPU and I/O costs. We develop new algorithms to answer proximity queries over objects that lie in the one-dimensional space (e.g., words in a document). The algorithms exploit query semantics to reduce the CPU and I/O costs, and hence improve performance. We also show how our algorithms can be generalized to handle d-dimensional objects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The increasing availability of massive and accurate laser data enables the processing of spatial queries on terrains. As shortest-path computation, an integral element of query processing, is inherently expensive on terrains, a key approach to enabling efficient query processing is to reduce the need for exact shortest-path computation in query processing. We develop new lower and upper bounds on terrain shortest distances that are provably tighter than any existing bounds. Unlike existing bounds, the new bounds do not rely on the quality of the triangulation. We show how use of the new bounds speeds up query processing by reducing the need for exact distance computations. Speedups of of nearly an order of magnitude are demonstrated empirically for well-known spatial queries.

Topographic maps, aerial and satellite imagery, relief maps, and stereoscopic anaglyphs have all been used to aid the understanding of the earth surface and geomorphic processes. Opportunities for incorporating new digital terrain data and virtual globes are reviewed and presented in a case study advanced university geomorphology course. The course uses physiographic divisions and provinces for the organization and intensive analysis of regional topography, landforms, and geographic variation of processes. Virtual globes' applications in lectures, student activities, and visual analysis are examined. Online tools for accessing terrain data and analyzing topographic profiles and imagery are also demonstrated. Virtual globes and online digital terrain databases are rapidly maturing technologies that are immediately accessible and provide a range of instructional technology uses. Examples and feedback from initial course delivery identified logistical constraints and future opportunities for these geospatial tools in geography education.

Spatial analytical queries on road networks typically perform hundreds of thousands to several millions of shortest distance computations in the process of producing results. These queries require architectures that can compute a large number of network distances. Two architectures are evaluated on a variety of spatial analytical queries on road networks. The first architecture is a widely used hybrid architecture that uses a database to store spatial datasets, a road network distance computing module, and an analysis tool to tie them together into a single query processing pipeline. The second architecture uses of a distance oracle representation of a road network. This architecture stores the spatial datasets and the distance oracle inside the database, and the query processing is completely handled by the database. A detailed evaluation of the two architectures for a variety of analytical query processing tasks such as region, KNN, distance matrix and trajectory queries is presented and the lessons learned are discussed.

Distributed computation of the knn graph for large high-dimensional point sets

The prevalence of computer graphics technology boosts the development of point clouds, which offer advantages over T riangular I rregular N etworks , i.e., TIN s, in proximity queries. All existing on-the-fly shortest path query algorithms and oracles on a TIN are expensive, and no algorithms can answer shortest path queries on a point cloud directly. Thus, we propose two types of efficient shortest path oracles on a point cloud. They answer the shortest path query between (1) a pair of P oints- O f- I nterests ( POIs ), and (2) any point and a POI, respectively. We propose four adaptations of them to answer the query between any point and a POI (or any point if no POIs are given). We also propose two efficient proximity query algorithms using these oracles. Our two oracles and their proximity query algorithms outperform the best-known adapted oracle by 12 to 42,000 times in terms of the oracle construction time, oracle size and proximity query time, respectively.

An approach is proposed to estimate the net radiation load at the surface in mountain areas. The components of the radiation balance are derived using a radiative transfer model combined with remotely sensed and digital terrain data. Integrated shortwave (0.28–6.00 µm) and longwave irradiances (3.00–100.00 µm) are computed using a modified version of the Practical Improved Flux Method (PIFM) of Zdunkowski et al. (1982) which makes use of digital topographic data in order to account for slope, aspect, and shading effects. Surface albedo and thermal exitance estimates are obtained using Landsat Thematic Mapper (TM) and digital terrain data combined with the LOWTRAN 7 atmospheric model (Kneizys et al., 1988). LOWTRAN 7 is utilized together with a set of terrain modeling programs to compute direct and diffuse sky irradiance for selected TM bands, and to remove atmospheric effects within the visible, near-infrared, mid-infrared, and thermal infrared bands of Landsat TM. Model testing in the Colorado alpine show a generally good correspondence between estimated values and field measurements obtained over comparable tundra surfaces during several field campaigns. The method is finally used to produce 1) maps of the components of the radiation balance at the time of Landsat TM overflight and 2) maps of daily totals of shortwave irradiance and net shortwave radiation on a typical summer day in the Colorado Rocky Mountains (i.e. including cloud cover effects). The results indicate that the proposed approach is particularly suitable for obtaining estimates of net radiation at the surface from the toposcale to the regional scale.