Using Images to create a Hierarchical Grid Spatial Index

This paper presents a hybrid approach to spatial indexing of two dimensional data. It sheds new light on the age old problem by thinking of the traditional algorithms as working with images. Inspiration is drawn from an analogous situation that is found in machine and human vision. Image processing techniques are used to assist in the spatial indexing of the data. A fixed grid approach is used and bins with too many records are sub-divided hierarchically. Search queries are pre-computed for bins that do not contain any data records. This has the effect of dividing the search space up into non rectangular regions which are based on the spatial properties of the data. The bucketing quad tree can be considered as an image with a resolution of two by two for each layer. The results show that this method performs better than the quad tree if there are more divisions per layer. This confirms our suspicions that the algorithm works better if it gets to look at the data with higher resolution images. An elegant class structure is developed where the implementation of concrete spatial indexes for a particular data type merely relies on rendering the data onto an image.Comment: In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Taiwan, 2006, pp. 1974-197

Adaptive Processing of Spatial-Keyword Data Over a Distributed Streaming Cluster

The widespread use of GPS-enabled smartphones along with the popularity of micro-blogging and social networking applications, e.g., Twitter and Facebook, has resulted in the generation of huge streams of geo-tagged textual data. Many applications require real-time processing of these streams. For example, location-based e-coupon and ad-targeting systems enable advertisers to register millions of ads to millions of users. The number of users is typically very high and they are continuously moving, and the ads change frequently as well. Hence sending the right ad to the matching users is very challenging. Existing streaming systems are either centralized or are not spatial-keyword aware, and cannot efficiently support the processing of rapidly arriving spatial-keyword data streams. This paper presents Tornado, a distributed spatial-keyword stream processing system. Tornado features routing units to fairly distribute the workload, and furthermore, co-locate the data objects and the corresponding queries at the same processing units. The routing units use the Augmented-Grid, a novel structure that is equipped with an efficient search algorithm for distributing the data objects and queries. Tornado uses evaluators to process the data objects against the queries. The routing units minimize the redundant communication by not sending data updates for processing when these updates do not match any query. By applying dynamically evaluated cost formulae that continuously represent the processing overhead at each evaluator, Tornado is adaptive to changes in the workload. Extensive experimental evaluation using spatio-textual range queries over real Twitter data indicates that Tornado outperforms the non-spatio-textually aware approaches by up to two orders of magnitude in terms of the overall system throughput

Ranking spatial data by quality preferences

A spatial preference query ranks objects based on the qualities of features in their spatial neighborhood. For example, using a real estate agency database of flats for lease, a customer may want to rank the flats with respect to the appropriateness of their location, defined after aggregating the qualities of other features (e.g., restaurants, cafes, hospital, market, etc.) within their spatial neighborhood. Such a neighborhood concept can be specified by the user via different functions. It can be an explicit circular region within a given distance from the flat. Another intuitive definition is to assign higher weights to the features based on their proximity to the flat. In this paper, we formally define spatial preference queries and propose appropriate indexing techniques and search algorithms for them. Extensive evaluation of our methods on both real and synthetic data reveals that an optimized branch-and-bound solution is efficient and robust with respect to different parameters. © 2006 IEEE.published_or_final_versio

The Stellar decomposition: A compact representation for simplicial complexes and beyond

We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex’s vertices and cells such that each region has sufficient information to locally reconstruct the star of its vertices, i.e., the cells incident in the region’s vertices. Stellar decompositions are general in that they can compactly represent and efficiently traverse arbitrary complexes with a manifold or non-manifold domain. They are scalable to complexes in high dimension and of large size, and they enable users to easily construct tailored application-dependent data structures using a fraction of the memory required by a corresponding global topological data structure on the complex. As a concrete realization of this model for spatially embedded complexes, we introduce the Stellar tree, which combines a nested spatial tree with a simple tuning parameter to control the number of vertices in a region. Stellar trees exploit the complex’s spatial locality by reordering vertex and cell indices according to the spatial decomposition and by compressing sequential ranges of indices. Stellar trees are competitive with state-of-the-art topological data structures for manifold simplicial complexes and offer significant improvements for cell complexes and non-manifold simplicial complexes. We conclude with a high-level description of several mesh processing and analysis applications that utilize Stellar trees to process large datasets

Indexing for efficient main memory processing

Ph.DDOCTOR OF PHILOSOPH

Tetrahedral Trees: A Family of Hierarchical Spatial Indexes for Tetrahedral Meshes

We address the problem of performing efficient spatial and topological queries on large tetrahedral meshes with arbitrary topology and complex boundaries. Such meshes arise in several application domains, such as 3D Geographic Information Systems (GISs), scientific visualization, and finite element analysis. To this aim, we propose Tetrahedral trees, a family of spatial indexes based on a nested space subdivision (an octree or a kD-tree) and defined by several different subdivision criteria. We provide efficient algorithms for spatial and topological queries on Tetrahedral trees and compare to state-of-the-art approaches. Our results indicate that Tetrahedral trees are an improvement over R*-trees for querying tetrahedral meshes; they are more compact, faster in many queries, and stable at variations of construction thresholds. They also support spatial queries on more general domains than topological data structures, which explicitly encode adjacency information for efficient navigation but have difficulties with domains with a non-trivial geometric or topological shape