J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems (TODS), 9(1):38--71, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....A search for existing data structures reveals that not many data structures exist that can fulfill the above requirements. Even commercial databases use rather old fashioned data structures. The ones considered were K D B trees, splay trees, several other trees, and Grid files. Grid files [129] fulfill the above requirements and were chosen for the implementation of the attribute index. The assumptions for the application of the Grid file concept hold for the receiver s DSU: the indexed objects (shipments, samples) have a small number of attributes (10) each attribute has a large ....

J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The Grid file: an adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9(1):38--71, 1984.

....special path based dimension keys are exploited. In particular, these keys guide the clustering (called chunking) process. Star joins are transformed to range queries in the multidimensional and multi level data space of a cube. The adopted multidimensional structure is a variant of the Grid File [NHS84]. Several aspects of processing and optimizing star join queries on hierarchically clustered fact tables are also presented in [TT01] The paper considers a star schema with UB Tree organized fact tables and dimension tables stored sorted on a composite surrogate key. For a particular class of ....

J. Nievergelt, H. Hinterberger, K. C. Sevcik: The Grid File: An Adaptable, Symmetric Multikey File Structure. TODS 9(1): 38-71 (1984)

....multiple dimensions simultaneously: they are known as multidimensional index structures. Work on multidimensional index structures dates back to early 1980s. The first multidimensional index structures to be proposed were the spatial index structures (e.g. R tree [59] kDB tree [120] grid file [105]) Although the above index structures work well at the low dimensional spaces (2 5 dimensions) which they are designed for, they are not suitable for high dimensional spaces that arise in modern database applications like multimedia retrieval (e.g. 64 d color histograms) data mining OLAP (e.g. ....

....corresponds to a range or k NN search on that data structure. To support efficient similarity search in a database system, robust techniques to index high dimensional feature spaces needs to be developed. Traditional multidimensional data structures (e.g. R trees [59] kDB trees [120] grid files [105]) which were designed for indexing spatial data, are not suitable for multimedia feature indexing due to (1) inability to scale to high dimensionality and (2) lack of support for queries based on arbitrary distance measures. Recently, there has been significant research effort in developing ....

J. Nievergelt, H. Hinterberger, and K.C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems(TODS), 1984.

....since every node has exactly horizontal and vertical neighbors. This simplifies the problem, e.g. for compilers that automatically parallelize code, and in fact partitionings are part of the High Performance Fortran 2. 0 standard [13] Another advantage, important for example in grid files [28] and certain classes of histograms [1, 11] is that the partitioning is uniquely defined by coordinates along the axis and coordinates along the axis. Thus, tiles can be indexed very efficiently by these coordinates. This simple structure also enables optimizations for cases where ....

.... of partitionings by running an algorithm along the rows and columns in a way that is slightly similar to our approach (though maybe not related in any formal way) Another scenario in databases is the construction of Grid File index structures for multi dimensional data, introduced in [28], where the goal is to limit the number of items in each tile. A significant amount of work on partitionings has been performed in the area of parallel computing, often under the term Generalized Block Distribution. In particular, 21, 27] propose heuristic algorithms for partitionings, ....

J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9(1), 38--71, 1984.

....procedures until Sections 4.2 and 4.4, respectively. h h Final hash value = 0100b = 4 (P.x) 00b (P.y) 01b y x h y h x P Figure 4: Using two hash functions to handle a 2D point. Each hash function will be used to hash one coordinate. LSH is very similar to Nievergelt s grid file [29,50]. However, the grid file was specifically designed to handle dynamic data, whereas LSH must be modified in order to do the same. Also, the grid file is more suitable for range searches than it is for solving the kNN problem. 3.2 Block Oriented Memory Model It has been our philosophy that ....

....shifted towards one end and packed into the leaf nodes. After compaction, empty nodes are discarded along with the rest of the tree index, while non empty nodes become photon blocks. are after; any other data structures that can group photons into spatially coherent groups, such as grid files [29,50], can be used in place of the B tree and space filling curve. Other techniques could of course be used for sorting. Another approach would be to store photons sequentially in a linked list of blocks as they are generated, and then sort the photons using a sequential access algorithm, such as ....

J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The Grid File: an adaptable, symmetric multikey file structure. ACM TODS, 9(1):38--71, March 1984. 4, 4.1

....Most spatial data structures in GIS are based on some hierarchical partitioning scheme of space [Sam90b] In this context, the divide and conquer principle is one of the strategies that is very helpful for designing an efficient spatial data structure. With the exception of the grid file [HN83, NHS84] and a few other structures, which use a general form of addressing techniques for multi dimensional data, we observe that spatial data structures which are based on the recursive partitioning of the object space dominate among those used today in large GIS [Sam90a, Wid91a, NW96] Since the ....

J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The Grid File: An Adaptable, Symmetric Multikey File Structure. ACM Trans. on Database Systems, 9:38--71, 1984.

.... systems [5, 8, 10] visual language parsers [7] VLSI design rule checkers [14] require a query language in which queries and integrity constraints may be expressed over a number of variables subject to Boolean constraints (that is, constraints over sets) In contrast, spatial data structures [6, 9, 12, 13] generally support only range queries . These are queries over a single unknown variable x of the form x a; b x; x Delta c 6= where a, b, and c are given bounding boxes. A bounding box is a rectangular region with sides parallel to the axes) Here, we give a query optimization technique ....

J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: an adaptable, symmetric multi-key file structure. ACM Trans. on Database Systems, 9(1):38--71, 1984.

....digital libraries for example, recently there have been proposals for GIS applications to handle queries with more complex and accurate structures, such as polygons. Numerous index structures have been developed to facilitate range searching in two and higher dimensions including grid files [NHK84] quadtrees [Sam89] kdb trees [Rob81] hB trees [LS90] R trees and variants [Gut84, BKSS90, BKK96] Another very important class of queries in applications that involve spatial data is that of nearest neighbor (NN) queries [RKV95] Similar to range queries, nearest neighbor queries are also ....

J. Nievergelt, H. Hinterberger, and K.C.Sevcik. The grid file: an adaptable, symmetric multikey file structure. ACM Transactions on Database Systems 9, 1:38--71, March 1984.

....information technology. In these applications, the data objects are represented as two dimensional feature vectors, and the similarity between objects are defined by a distance function between corresponding feature vectors. Several index structures have been proposed for retrieval of spatial data [20, 11, 16, 19, 12, 1]. The common approach is to group the objects according to their spatial locations and store the created groups as pages in physical storage. Most of the approaches in the literature for indexing spatial data are based on clustering data points with a rectangular organization [20, 11, 12, 1] ....

....spatial data are based on clustering data points with a rectangular organization [20, 11, 12, 1] There have been several approaches for the storage and retrieval of spatial data based on partitioning the data space. Grid based file structures have been effectively used to index spatial data [16], and there have been several approaches based on the grid partitioning [20, 11] Because of their simplicity in hashing and mapping to physical storage, regular equi sized partitioning are widely used for retrieval and storage of spatial data. A common example of such techniques is the regular ....

J. Nievergelt, H. Hinterberger, and K.C.Sevcik. The grid file: an adaptable, symmetric multikey file structure. ACM Transactions on Database Systems 9, 1:38--71, March 1984.

....of type string, numeric, date, etc. It is widely believed that relational databases would not have enjoyed the popularity they enjoy, had the B tree not accompanied them with such superb timing. Analogous events took place in the mid 80 s, when the development of structures such as the grid file [NHS84] the kd B tree [Rob84] and of course the R tree [Gut85] launched the era of Geographic Information Systems (GIS) by supporting e#cient multi dimensional range searching for geographic data. In subsequent years, a plethora of techniques was developed, including extensions of the R tree, ....

.... most notably the kd B tree [Rob84] the hB tree [LS90] and the LSD tree [HSW89] Apart from these, which were 23 discussed in the previous section, the majority of the multidimensional access methods can trace their ancestry to one or more of the following three techniques: the grid file [NHS84] z ordering [OM84] and the R tree [Gut85] We survey briefly the main ideas behind these techniques and their many refinements. For more complete surveys, we recommend the paper by Gaede and Gunther [GG98] which focuses on spatial access methods, and also that of Salzberg and Tsotras [ST99] ....

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J. Nievergelt, H. Hinterberger, and K.C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9(1):257--276, 1984. 176

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems (TODS), 9(1):38--71, 1984.

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 1984.

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Nievergelt, J., Hinterberger, H., and Sevcik, K.C. The grid file: an adaptable, symmetric multikey file structure. ACM Trans. on database systems 9, 1 (1984), pp. 38-71.

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J. Nievergelt, H. Hinterberger, K. C. Sevcik: The Grid File: An Adaptable, Symmetric Multikey File Structure. ACM Trans. on Database Systems, 9(1), 1984, pages 38-71.

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Nievergelt, J., Hintenberger, H. and Sevcik, K. The Grid File: An Adaptable, Symmetric Multikey File Structure. ACM Trans. on Database Systems, Vol.9, No.1, 1984.

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Jurg Nievergelt, Hans Hinterberger, and Kenneth C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions On Database Systems, 9(1):38--71, 1984.

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Nievergelt, J.; Hinterberger, H.; Sevcik, K.C.: The Grid File: An Adaptable, Symmetric Multikey File Structure, in: ACM Transactions on Database Systems 9(1984)1, pp. 38-71

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9(1):38--71, 1984.

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J. Nievergelt, H. Hinterberger, and K.C. Sevcik. The grid file: an adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9(1):38--71, 1984.

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J. Nievergelt, H. Hinterberger, and K.C.Sevcik. The grid file: an adaptable, symmetric multikey file structure. ACM Transactions on Database Systems 9, 1:38--71, Mar. 1984.

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Transactions on Database Systems, 9(1), 38--71, 1984.

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J. Nievergelt, H. Hinterberger and K. C. Sevcik, The Grid File: An Adaptable, Symmetric Multikey File Structure, ACM Trans. Database Systems 9,1 (Mar. 1984), 38-71.

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The Grid File: An Adaptable, Symmetric Multikey File Structure . TODS, 9(1):38--71, Mar. 1984.

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The grid file: An adaptable, symmetric multikey file structure. ACM Trans. on Database Systems, 9(1):38--71, Mar. 1984.

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J. Nievergelt, H. Hinterberger, and K. C. Sevcik. The Grid File: an adaptable, symmetric multikey file structure. ACM TODS, 9(1):38--71, March 1984. 3, 5

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