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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 ..."
Abstract

Cited by 322 (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.
A DistanceScan Algorithm for Spatial Access Structures
, 1994
"... In geographic information systems it is often useful to select an object located closest to a given point or to scan the objects with respect to their distance to a given point in ascending order. An example for a query of this type would be to retrieve ten hotels with at least three stars lying clo ..."
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Cited by 32 (6 self)
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In geographic information systems it is often useful to select an object located closest to a given point or to scan the objects with respect to their distance to a given point in ascending order. An example for a query of this type would be to retrieve ten hotels with at least three stars lying closest to the venue of a conference. Various subtypes of similar queries exist. On the other hand, research in geometric access structures has concentrated mainly on range queries. We present an efficient algorithm for closest and distancescanqueries of various kinds. Our algorithm is based on the nearest neighbour algorithm for kdtrees given by Friedman et al. [FBF77] and refined by Sproull [Spr91]. We adapt this algorithm to external access structures and extend it to process a broader class of queries. Furthermore we show that the algorithm can be applied to point objects as well as to nonpoint objects, and that it can be used with all spatial access structures using a hierarchical dir...
Extending a spatial access structure to support additional standard attributes
, 1995
"... In recent years, many access structures have been proposed supporting access to objects via their spatial location. However, additional nongeometric properties are always associated with geometric objects, and in practice it is often necessary to use select conditions based on spatial and standard ..."
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Cited by 11 (4 self)
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In recent years, many access structures have been proposed supporting access to objects via their spatial location. However, additional nongeometric properties are always associated with geometric objects, and in practice it is often necessary to use select conditions based on spatial and standard attributes. An obvious idea to improve the performance of queries with mixed select conditions is to extend spatial access structures with additional dimensions for standard attributes. Whereas this idea seems to be simple and promising at rst glance, a closer look brings up serious problems, especially with select conditions containing arithmetic expressions or select conditions for nonpoint objects and with Boolean operators like or and not. In this paper we present a solution to overcome the problems sketched above which is based on three pillars: (1) We present powerful basic techniques to deal with arithmetic conditions containing mathematical operations (like `+', `;', ` ', and `=') and range queries for nonpoint objects. (2) We introduce a technique which allows to decompose select conditions containing Boolean operators and to reduce the processing of such a select condition to the processing of its elementary parts. (3) We showhow other operations like joins and distancescans can be integrated into this query processing architecture.
Are Window Queries Representative for Arbitrary Range Queries?
"... In this paper, we characterize the efficiency of spatial access structures in terms of the expected number of data bucket accesses needed to perform a range query. We derive performance formulas for various kinds of range queries like intersection, containment, and enclosure queries with different g ..."
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Cited by 10 (1 self)
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In this paper, we characterize the efficiency of spatial access structures in terms of the expected number of data bucket accesses needed to perform a range query. We derive performance formulas for various kinds of range queries like intersection, containment, and enclosure queries with different geometric shapes. The formulas exhibit that range query performance in general depends on three parameters: the area sum of the data regions, the perimeter sum, and the number of regions. Only the weights of these parameters vary from shape to shape and query type to query type. To a wide extent, our results prove the conjecture that window queries are representative for range queries in general.
A Region Splitting Strategy for Physical Database Design of Multidimensional File Organizations
 IN PROC. THE 23RD INT’L CONF. ON VERY LARGE DATA BASES
, 1997
"... This paper presents a region splitting strategy for physical database design of multidimensional file organizations. Physical database design is the process of determining the optimal configuration of physical files for a given set of queries. Recently, many multidimensional le organizations for sup ..."
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Cited by 10 (5 self)
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This paper presents a region splitting strategy for physical database design of multidimensional file organizations. Physical database design is the process of determining the optimal configuration of physical files for a given set of queries. Recently, many multidimensional le organizations for supporting multiattribute access have been proposed in the literature. However, there has been no effort for their physical database design. We first show that the performance of query processing is highly affected by the similarity between the shapes of query regions and page regions in the domain space, and then propose a new region splitting strategy that finds the optimal configuration of the multidimensional file by controlling the interval ratio of different axes to achieve the similarity. Wealso present the results of extensive experiments using the multilevel grid file (MLGF), a multidimensional file organization, and various types of
Adapting the Transformation Technique to Maintain MultiDimensional NonPoint Objects in kdTree Based Access Structures
 PROC. 3RD ACM INT. WORKSHOP ON ADVANCES IN GEOGRAPHIC INFORMATION SYSTEMS (ACMGIS '95)
, 1995
"... In [10, 18] the transformation technique has been proposed to store kdimensional intervals  which serve as bounding boxes for arbitrary geometric objects in many applications  as 2kdimensional points in a point access structure. Unfortunately the transformation technique has two pitfalls: (1) ..."
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Cited by 4 (0 self)
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In [10, 18] the transformation technique has been proposed to store kdimensional intervals  which serve as bounding boxes for arbitrary geometric objects in many applications  as 2kdimensional points in a point access structure. Unfortunately the transformation technique has two pitfalls: (1) The transformation leads to a skew distribution of the 2kdimensional image points. (2) Processing a range query searching all objects intersecting a given query region, there is a mismatch between thekdimensional query region and the 2kdimensional access structure. In this paper we propose two techniques to overcome these problems which can be directly applied tokdtree based point access structures: (1) We present a sophisticated split strategy to determine the split dimension and the split position in case of a bucket split which exploits the knowledge about the distribution of the image points of the transformation technique to gain an extremely exible and robust access structure. (2) We propose a retransformation of the 2kdimensional data regions in the access structure into the originalkdimensional data space in order to compare these regions with thekdimensional query region. Furthermore we state experimental results, which demonstrate, that the presented techniques allow to maintainkdimensional nonpoint objects with nearly the same performance as kdimensional point objects.
Efficient Window Block Retrieval in QuadtreeBased Spatial Databases
 GeoInformatica
, 1996
"... An algorithm is presented to answer window queries in a quadtreebased spatial database environment by retrieving all of the quadtree blocks in the underlying spatial database that cover the quadtree blocks that comprise the window. It works by decomposing the window operation into suboperations ov ..."
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Cited by 4 (2 self)
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An algorithm is presented to answer window queries in a quadtreebased spatial database environment by retrieving all of the quadtree blocks in the underlying spatial database that cover the quadtree blocks that comprise the window. It works by decomposing the window operation into suboperations over smaller window partitions. These partitions are the quadtree blocks corresponding to the window. Although a block b in the underlying spatial database may cover several of the smaller window partitions, b is only retrieved once rather than multiple times. This is achieved by using an auxiliary main memory data structure called the active border which requires O(n) additional storage for a window query of size n \Theta n. As a result, the algorithm generates an optimal number of disk I/O requests to answer a window query (i.e., one request per covering quadtree block). A proof of correctness and an analysis of the algorithm's execution time and space requirements are given, as are some ex...
Die Nutzung mehrdimensionaler Zugri sstrukturen fur Standardattribute
 In Proc. GIFachtagung Datenbanksysteme in Buro, Technik und Wissenschaft
, 1995
"... ..."
Contents
"... Search operations in databases require some special support at the physical level. This is true for conventional databases as well as for spatial databases, where typical search operations include the point query ( nd all objects that contain a given search point) and the region query ( nd all objec ..."
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Search operations in databases require some special support at the physical level. This is true for conventional databases as well as for spatial databases, where typical search operations include the point query ( nd all objects that contain a given search point) and the region query ( nd all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great varietyofmultidimensional access methods to support such operations. This paper gives an overview of that work. After a brief survey of spatial data management in general, we rst present the class of point access methods, which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results