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Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 306 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Scalable Network Distance Browsing in Spatial Databases
, 2008
"... An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact ..."
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Cited by 50 (8 self)
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An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact that the shortest paths from vertex u to all of the remaining vertices can be decomposed into subsets based on the first edges on the shortest paths to them from u. Thus, in the worst case, the amount of work depends on the number of objects that are examined and the number of links on the shortest paths to them from q, rather than depending on the number of vertices in the network. The amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree. In particular, experiments on a number of large road networks as
A Qualitative Comparison Study of Data Structures for Large Line Segment Databases
, 1992
"... A qualitative comparative study is performed of the performance of three popular spatial indexing methods  the r tree, r + tree, and the pmr quadtree  in the context of processing spatial queries in large line segment databases. The data is drawn from the tiger/Line files used by the Bure ..."
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Cited by 49 (6 self)
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A qualitative comparative study is performed of the performance of three popular spatial indexing methods  the r tree, r + tree, and the pmr quadtree  in the context of processing spatial queries in large line segment databases. The data is drawn from the tiger/Line files used by the Bureau of the Census to deal with the road networks in the US. The goal is not to find the best data structure as this is not generally possible. Instead, their comparability is demonstrated and an indication is given as to when and why their performance differs. Tests are conducted with a number of large datasets and performance is tabulated in terms of the complexity of the disk activity in building them, their storage requirements, and the complexity of the disk activity for a number of tasks that include point and window queries, as well as finding the nearest line segment to a given point and an enclosing polygon. 1 Introduction Spatial data consists of points, lines, regions, rectangles,...
Scalability analysis of declustering methods for multidimensional range queries
 IEEE Trans. on Knowledge and Data Eng
, 1998
"... Abstract—Efficient storage and retrieval of multiattribute data sets has become one of the essential requirements for many dataintensive applications. The Cartesian product file has been known as an effective multiattribute file structure for partialmatch and bestmatch queries. Several heuristic ..."
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Cited by 32 (18 self)
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Abstract—Efficient storage and retrieval of multiattribute data sets has become one of the essential requirements for many dataintensive applications. The Cartesian product file has been known as an effective multiattribute file structure for partialmatch and bestmatch queries. Several heuristic methods have been developed to decluster Cartesian product files across multiple disks to obtain high performance for disk accesses. Although the scalability of the declustering methods becomes increasingly important for systems equipped with a large number of disks, no analytic studies have been done so far. In this paper, we derive formulas describing the scalability of two popular declustering methods¦Disk Modulo and Fieldwise Xor¦for range queries, which are the most common type of queries. These formulas disclose the limited scalability of the declustering methods, and this is corroborated by extensive simulation experiments. From the practical point of view, the formulas given in this paper provide a simple measure that can be used to predict the response time of a given range query and to guide the selection of a declustering method under various conditions.
Explicit Graphs in a Functional Model for Spatial Databases
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 1994
"... 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 ordersorted algebra. Besides object and data type hierarchies grap ..."
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Cited by 29 (9 self)
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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 ordersorted 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 multilevel ordersorted 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.
Analysis of ndimensional Quadtrees Using the Hausdorff Fractal Dimension
 In Proc. 22nd Int. Conf. on Very Large Data Bases
, 1996
"... There is mounting evidence [Man77, Sch91] that real datasets are statistically selfsimilar, and thus, `fractal'. This is an important insight since it permits a compact statistical description of spatial datasets; subsequently, as we show, it also forms the basis for the theoretical analysis o ..."
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Cited by 21 (2 self)
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There is mounting evidence [Man77, Sch91] that real datasets are statistically selfsimilar, and thus, `fractal'. This is an important insight since it permits a compact statistical description of spatial datasets; subsequently, as we show, it also forms the basis for the theoretical analysis of spatial access methods, without using the typical, but unrealistic, uniformity assumption. In this paper, we focus on the estimation of the number of quadtree blocks that a real, spatial dataset will require. Using the the wellknown Hausdorff fractal dimension, we derive some closed formulas which allow us to predict the number of quadtree blocks, given some few parameters. Using our formulas, it is possible to predict the space overhead and the response time of linear quadtrees/zordering [OM88], which are widely used in practice. In order to verify our analytical model, we performed an extensive experimental investigation using several real datasets coming from different domains. In these ex...
Spatial Data Models and Query Processing
 Modern Database Systems
, 1994
"... An overview is presented of the issues in building spatial databases. The focus is on data models and query processing. Query optimization in a spatial environment is also briefly discussed. Keywords and phrases: spatial databases, data models, spatial query processing, spatial query optimization, r ..."
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Cited by 20 (4 self)
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An overview is presented of the issues in building spatial databases. The focus is on data models and query processing. Query optimization in a spatial environment is also briefly discussed. Keywords and phrases: spatial databases, data models, spatial query processing, spatial query optimization, relational databases. This work was supported in part by the National Science Foundation under Grant IRI9017393. To appear in Modern Database Systems: The Object Model, Interoperability, and Beyond, W. Kim, ed., Addison Wesley/ACM Press, Reading, MA, 1994. 1 Introduction Not so long ago the term database management system (DBMS) was a euphemism for distinguishing commercial applications (e.g., banking, insurance, etc.) from scientific applications (e.g., number crunching). Today the distinction is rapidly disappearing as users try to come to grips with an information explosion that increasingly involves the world around them. Some new application areas include geographic information sys...
Clustering techniques for minimizing external path length
 Proceedings of the International Conference on Very Large Databases
, 1996
"... There are a variety of mainmemory access structures, such as segment trees, and quad trees, whose properties, such as good worstcase behaviour, make them attractive for database applicdions. Unfortunately, the structures are typically ‘long and skinny’, whereas disk data structuies must be ‘short ..."
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Cited by 17 (0 self)
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There are a variety of mainmemory access structures, such as segment trees, and quad trees, whose properties, such as good worstcase behaviour, make them attractive for database applicdions. Unfortunately, the structures are typically ‘long and skinny’, whereas disk data structuies must be ‘shortandfat (that is, have a high fanout and low height) in order to minimize I/O. We consider how to cluster the nodes (that is, map the nodes to disk pages) of mainmemory access structures such that although a path may traverse many nodes, it only traverses a few disk pages. The number of disk pages traversed in a path is called the external path length. We address several versions of the clustering problem. We present a clustering algorithm for tree structures that generates optimal worstcase external path length mappings; we also show how to make it dynamic, to support updates. We extend the algorithm to generate mappings that minimize the average weighted external path lengths. We also show that some other clustering problems, such as finding optimal external path lengths for DAG structures and minimizing
Further Comparison of Algorithms for Geometric Intersection Problems
 In Proc. 6th Int'l. Symp. on Spatial Data Handling
, 1994
"... The usual first step in computing an overlay of two vector maps is to determine which pairs of segments (one from each map) intersect so as to perform linebreaking. We identify two classes of algorithms for the segment intersection problem, spatial partitioning and spatial ordering, and we report o ..."
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Cited by 12 (2 self)
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The usual first step in computing an overlay of two vector maps is to determine which pairs of segments (one from each map) intersect so as to perform linebreaking. We identify two classes of algorithms for the segment intersection problem, spatial partitioning and spatial ordering, and we report on implementations of seven algorithms, some known and some new. Though the spatial ordering algorithms can be made output sensitive, our experiments show that the spatial partitioning algorithms are better for segment intersection in a GIS context. We do identify a new Trapezoid Sweep algorithm that is competitive if the segments are stored in sorted order. 1 Introduction Map overlay processing is at the core of most vectorbased Geographic Information Systems (GISs). One of the timeconsuming steps of this processing is linebreaking, which we can abstract as the segment intersection problem: Given a collection of n line segments in the plane, determine which pairs intersect. For overlay...
Analysis of the nDimensional Quadtree Decomposition for Arbitrary Hyperrectangles
 TKDE
, 1997
"... We give a closedform expression for the average number of ndimensional quadtree nodes ("pieces" or "blocks") required by an ndimensional hyperrectangle aligned with the axes. Our formula includes as special cases the formulae of previous efforts for twodimensional spaces [8]. ..."
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Cited by 11 (2 self)
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We give a closedform expression for the average number of ndimensional quadtree nodes ("pieces" or "blocks") required by an ndimensional hyperrectangle aligned with the axes. Our formula includes as special cases the formulae of previous efforts for twodimensional spaces [8]. It also agrees with theoretical and empirical results that the number of blocks depends on the hypersurface of the hyperrectangle and not on its hypervolume. The practical use of the derived formula is that it allows the estimation of the space requirements of the ndimensional quadtree decomposition. Quadtrees are used extensively in twodimensional spaces (geographic information systems and spatial databases in general), as well in higher dimensionality spaces (as octtrees for threedimensional spaces, e.g., in graphics, robotics, and threedimensional medical images [2]). Our formula permits the estimation of the space requirements for data hyperrectangles when stored in an index structure like a (ndimensional) quadtree, as well as the estimation of the search time for query hyperrectangles, for the socalled linear quadtrees [17]. A theoretical contribution of the paper is the observation that the number of blocks is a piecewise linear function of the sides of the hyperrectangle.