L. Becker, K. Hinrichs, and U. Finke. A New Algorithm for Computing Joins With Grid Files. In Proceedings of International Conference on Data Engineering, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and Forest Stand relations, based on their spatial attributes. A spatial join is more complex than an equi join and is a special case of a Theta join, where Theta is a spatial predicate, e.g. touch, overlap, and cross. The query Q is an example of a spatial join. A spatial join algorithm [2, 5, 6, 16, 30] may be used to find the pairs (Facility, Forest stand) which satisfy query Q. Alternatively, a join index may be used to materialize a subset of the result to speed up processing for the future occurrence of Q, if there are few updates to the spatial data. Figure 1(b) shows a join index with two ....

L. Becker, K. Hinrichs, and U. Finke. A New Algorithm for Computing Joins With Grid Files. In Proceedings of International Conference on Data Engineering, 1993.

....[Gun93] proposed a general method using generalization trees as index structures for evaluating joins with many predicates including intersection, On Multi Way Spatial Joins with Direction Predicates 219 direction, distance, etc. Becker, Hinrichs, and Finke used grid file to compute spatial joins [BHF93] These algorithms uses data structures that cannot guarantee better I O complexity in the worst case. In fact, in the worst case the I O cost of these join algorithms is still O(N 2 ) There is no other work on spatial joins with direction predicates to the best of our knowledge. Spatial ....

L. Becker, K. Hinriches, and U. Finke. A new algorithm for computing joins with grid files. In Proc. Int. Conf. on Data Engineering, pages 190-- 197, 1993.

....; YLL ) and the upper right corner point(XUR ; YUR ) Now, consider the following query: Q: Find all forest stands which are within a distance D from a facility . This query will require a join on the Facility and Forest Stand relations based on their spatial attributes, Spatial join algorithm [1, 4, 5, 14, 23] may be used to find the pairs (Facility, Forest stand) which satisfy the query Q. Alternatively, a join index may be used to materialize a subset of result to speed up processing for future occurrence of Q if there are few updates to spatial data and the query Q is frequently requested. Figure ....

L. Becker, K. Hinrichs, and U. Finke. A New Algorithm for Computing Joins With Grid Files. In Proceedings of International Conference on Data Engineering, 1993.

....road network and land use databases are given in Figure 2) As pointed out in [8] both the CPU and the disk read costs of the spatial join operation are very significant. As a result, extensive research has been conducted on alternative ways of processing the spatial join efficiently (e.g. see [6, 7, 8, 16, 27, 30]) Becker [7] and Becker, Hinrichs, and Finke [6] propose an algorithm for the efficient evaluation of spatial join for databases of point objects. Gunther [16] presents a hierarchical spatial join algorithm that applies efficiently for a family of tree based data structures, termed the ....

....out in [8] both the CPU and the disk read costs of the spatial join operation are very significant. As a result, extensive research has been conducted on alternative ways of processing the spatial join efficiently (e.g. see [6, 7, 8, 16, 27, 30] Becker [7] and Becker, Hinrichs, and Finke [6] propose an algorithm for the efficient evaluation of spatial join for databases of point objects. Gunther [16] presents a hierarchical spatial join algorithm that applies efficiently for a family of tree based data structures, termed the generalization tree. Brinkhoff, Kriegel, and Seeger [8] ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In Proc. of the 9th Intl. Conf. on Data Engr., pp. 190--197, Vienna, Austria, Apr. 1993.

....access 120 60 0 60 120 180 5,000 50,000 500,000 longitude 60 30 0 30 60 90 latitude population Fig. 1. Data space for an access structure for a spatial and a standard attribute structures (see e.g. Hen94] and even joins based on spatial join conditions can be supported (see e.g. [BHF93]) However, additional non geometric properties are always associated with geometric objects, and in practice it is often necessary to use select conditions based on spatial and standard attributes. Atypical situation is the following: Suppose our database contains a relation (or class) Cities ....

....one relation is maintained by an LSD tree. For other multi dimensional structures methods for executing equi joins have been proposed, e.g. in [OB88, CFMT86, TRN86]# [KHT89]even considers k d trees. For more complex joins, we only know of one approach for grid files [NHS84] which is presented in [BHF93]. ....

L. Becker, K. Hinrichs, and U. Finke. A New Algorithm for Computing Joins with Grid Files. In Proc. IEEE Int'l. Conf. on Data Eng., pages 190-- 197, Vienna, Austria, April 1993.

.... step returns a candidate set that contains answers (hits) and additionally elements of the Cartesian product which do not fulfill the join predicate (false hits) This step should be supported by spatial access methods (SAMs) Recently, several papers on MBR joins using SAMs were published, e.g. BHF 93] Gn 93] BKS 93a] and [LR 94] In the second step (approximation step) more accurate approximations are exploited for filtering out false hits from the candidate set. Moreover, approximations can also be used to identify hits without accessing the exact representation of the spatial ....

Becker L., Hinrichs K., Finke U.: `A New Algorithm for Computing Joins with Grid Files', Proc. 9th Int. Conf. on Data Engineering, Vienna, Austria, 1993, pp. 190-197.

....an experimental comparison of Plug Join and PBSM using non artificial spatial data sets. 1. 1 Review of previous work Good surveys of algorithms for processing relational joins are provided in [Sha 86] ME 92] and [Gra 93] There has been quite a lot of work on spatial joins recently ( Ore 86] BFH 93] BKS 93] Gn 93] LR 94] HS 95] LR 96] PD 96] KS 97] APR 98] MP 99] The spatial join combines two sets of spatial objects with respect to a spatial predicate. Most of the mentioned work has dealt with intersection as the join predicate, but there is also the need to support ....

Becker, L.; Finke, U.; Hinrichs, K.: A New Algorithm for Computing Joins with Grid Files. ICDE 1993: 190-197

....has been described by Orenstein [Ore86] Abel et al. AOT 95] later extended this work to support spatial join processing in a distributed environment. Becker et al. store the bounding boxes of the spatial objects as points in a higher dimension and use a grid file to find matching pairs [BHF93] Another approach is to take advantage of the plane sweep technique known from computational geometry [PS85] Rotem [Rot91] uses this technique to build a spatial join index from existing grid files. Patel and DeWitt [PD96] partition the universe into tiles and use plane sweep to find matching ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In Proc. IEEE 9th Int. Conference on Data Engineering, 1993. 14

....performs a spatial join on approximations of the objects; and (2) a refinement step that checks whether the objects discovered by the filter step actually intersect. A great deal of research has been done to speed up the filter step and to reduce the size of the result it produces. Many algorithms [16, 18, 17, 20, 3, 7, 1, 19, 22, 15, 11, 2, 25] focus on the filter step and use the minimum bounding rectangle (MBR) the smallest rectangle containing a spatial object, as an approximation of the object. In this paper, we call these algorithms rectangle join algorithms. Rectangle join evaluation has been the focus of the study on spatial ....

....The existing algorithms can be classified into two categories. The first category includes algorithms that do not need any (spatial) index structures in addition to the input rectangles. In this category, the algorithms in [16 18] use a space filling curve, called z ordering; the algorithm in [3] transfers rectangles into points in the 4 dimension space and uses grid files to compute the join; both algorithms in [19, 15] use a partition based method. In addition, 2] uses a distributed sweeping technique [9] to achieve IO e#ciency. The algorithms in the second category requires additional ....

[Article contains additional citation context not shown here]

L. Becker, K. Hinriches, and U. Finke. A new algorithm for computing joins with grid files. In Proc. Int. Conf. on Data Engineering, 1993.

....no non horizontal boundary intersection) and the algorithm by Bentley and Ottmann [7] for the general case) for Step 1. We show that Step 2 can be done by modifying Step 1. However, Step 2 also restricts Step 3 to be done in a dynamic way. The new algorithm is needed since the existing algorithms [21, 23, 22, 26, 6, 9, 13, 18, 25, 27, 14, 2, 29] either increase the I O complexity or cannot be easily tailored to fully utilize the properties of the rectangles generated by Step 2. Detail discussions on the choices are provided in the technical presentation. The organization of this paper is as follows. Section 2 discusses approaches to ....

....presented in Section 3. Surprisingly, in Section 5, we show that trapezoid containment and intersections involving horizontal boundaries can be reduced to a restricted version of rectangle join using the ordering lists of non horizontal boundaries. This has a cost. The existing algorithms [21, 23, 22, 26, 6, 9, 13, 18, 25, 27, 14, 2, 29] either lead to high complexity or cannot be pipelined with the line segment intersection algorithm. For this reason, we develop a new rectangle join algorithm rjoin which can be extended for the restricted rectangle join. We show that rjoin evaluates a join of two sets of N rectangles in O(N log ....

[Article contains additional citation context not shown here]

L. Becker, K. Hinriches, and U. Finke. A new algorithm for computing joins with grid files. In Proc. Int. Conf. on Data Engineering, pages 190--197, 1993.

....catches all matching tuples during the following merge. One notable exception from this effect is the join predicate intersects , for which sort merge strategies can be used. Efficient implementations have been described, among others, by Orenstein [Ore86] Abel et al. AOT 95] and Becker [BHF93] In this paper we concentrate on three strategies to compute spatial joins: nested loop (NL) scan and index (SI) and synchronized tree traversal (STT) We discuss these approaches in turn. 2.3.1 Nested Loop (NL) The simple nested loop approach compares each tuple in R with each tuple in S. ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In Proc. IEEE 9th Int. Conference on Data Engineering, 1993.

....) and the upper right corner point(XUR ; YUR ) Now, consider the following query: Q: Find all forest stands which are within a distance D from each facility . This query will require a join on the Facility and Forest Stand relations, based on their spatial attributes. A spatial join algorithm [2, 3, 4, 12, 25] may be used to find the pairs (Facility, Forest stand) which satisfy query Q. Alternatively, a join index may be used to materialize a subset of the result to speed 1 up processing for the future occurrence of Q if there are few updates to the spatial data. Figure 1(b) shows a join index with ....

L. Becker, K. Hinrichs, and U. Finke. A New Algorithm for Computing Joins With Grid Files. In Proceedings of International Conference on Data Engineering, 1993.

....then performs a sort merge join along the curve. The performance of the resulting algorithm is sensitive to the size of the pixels chosen, in that smaller pixels leads to better filtering, but also increase the number of pixels associated with each object. In another transformational approach [BHF93] the MBRs of spatial objects (which are rectangles in two dimensions) are transformed into points in four dimensions. The resulting points are stored in a multi attribute data structure such as the grid file [NHS84] which is then used for the filter step. Rotem [Rot91] proposes a spatial join ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In International Conference on Data Engineering, pages 190--198, 1993. IEEE Computer Society Press.

....experimental results. Finally, Section 7 offers some concluding remarks. 2 Previous Work Early Work. Orenstein [29] uses a transformational approach based on space filling curves, and then performs a sort merge join along the curve to solve the join problem. In another transformational approach [6], the MBRs of two dimensional spatial objects are transformed into points in four dimensions. These points are stored in a multi attribute data structure such as the grid file [27] which is then used to perform the join. An efficient algorithm for the rectangle intersection problem based on ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In Proc. IEEE Intl. Conf. on Data Engineering, pages 190--197, 1993.

....then performs a sort merge join along the curve. The performance of the resulting algorithm is sensitive to the size of the pixels chosen, in that smaller pixels leads to better filtering, but also increase the number of pixels associated with each object. In another transformational approach [BHF93] the MBRs of spatial objects (which are rectangles in two dimensions) are transformed into points in four dimensions. The resulting points are stored in a multi attribute data structure such as the grid file [NHS84] which is then used for the filter step. Rotem [Rot91] proposes a spatial join ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In International Conference on Data Engineering, pages 190--198, 1993. IEEE Computer Society Press.

....Early Work. An early algorithm proposed by Orenstein [30] uses a space filling curve, called Peano curve or z ordering, to associate each rectangle with a set of small blocks, called pixels, on that curve, and then performs a sort merge join along the curve. In another transformational approach [5], the MBRs of twodimensional spatial objects are transformed into points in four dimensions. These points are stored in a multi attribute data structure such as the grid file [28] which is then used for the filter step. An efficient algorithm for the rectangle intersection problem based on the ....

L. Becker, K. H. Hinrichs, and U. A. Finke. A new algorithm for computing joins with grid files. In Proceedings of the Ninth International Conference on Data Engineering, pages 190--197. IEEE Computer Society, 1993.

....indexes. Since the processing of spatial predicates in a spatial relation is crucial in an SDBMS one can argue that indexes on those predicates should necessarily exist in order to efficiently support the basic (spatial) operations of the system. Among others, Grid files have been studied in [Rot91, BHF93] and R trees in [BKS93] We select the R tree structure to be the underlying index since it has been widely recognised as the most effective indexing method and has been incorporated in commercial database systems, such as Postgres [SRH90] and Illustra [Ube94] The basic idea on the implementation ....

L. Becker, K. Hinrichs, U. Finke, "A New Algorithm for Computing Joins with Grid Files", Proceedings of the 9th IEEE Conference on Data Engineering, 1993.

....has been described by Orenstein [Ore86] Abel et al. AOT 95] later extended this work to support spatial join processing in a distributed environment. Becker et al. store the bounding boxes of the spatial objects as points in a higher dimension and use a grid file to find matching pairs [BHF93] Another approach is to take advantage of the plane sweep technique known from computational geometry [PS85] Rotem [Rot91] uses this technique to build a spatial join index from existing grid files. Patel and DeWitt [PD96] partition the universe into tiles and use plane sweep to find matching ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In Proc. IEEE 9th Int. Conference on Data Engineering, 1993.

....are supported by spatial indexes. Since the processing of spatial predicates is crucial in an SDBMS, one can argue that indexes on those predicates should necessarily exist in order to efficiently support the basic (spatial) operations of the system. Among others, Grid files have been studied in [Rot91, BHF93] and R trees in [BKS93] We select the R tree structure to be the underlying index since it has been widely recognized as the most effective family of spatial indexing methods. 0 1 ( 0 1 q 5227 Figure 1: An example of R tree index. Figure 1 ....

L. Becker, K. Hinrichs, U. Finke, "A New Algorithm for Computing Joins with Grid Files", Proc. 9th IEEE Data Engineering Conf., 1993.

....the disk blocks in terms of the number of records that they can hold. 3 Several alternative organizations for the grid file directory control its growth and make it proportional to the data size. These alternative organizations include the region representation directory and the BR 2 directory [3]. The 2 level directory organization [20] shows how to implement the directory on disk. We have not yet explored how these techniques would work in our environment. 1. Compute region and block for record 2. If Record fits in block 3. Insert record 4. Else 5. If Usable partitions in database ....

....queries, where the queries involve disjunction as well as conjunction. There is more work to be done on the storage of these summaries as well. An unfortunate aspect of the grid files is their need for a relatively large directory. Techniques have been reported for controlling directory size [3]; we must examine whether those techniques are applicable to the highly skewed grid files generated by the GlOSS summaries. Compression techniques [42] would have a significant impact on the performance figures reported here. Finally, building an operational GlOSS server for a large number of ....

Ludger Becker, Klaus Hinrichs, and Ulrich Finke. A new algorithm for computing joins with grid files. In Proceedings of the 9 th International Conference on Data Engineering, pages 190--197, 1993.

.... 98] ii. two indices: when both relations are indexed, the algorithms that have been proposed depend on the SAM used. Ore86] is the first known work on spatial joins. It proposes a 1 dimensional ordering of spatial objects, which are then indexed on their rank in a B tree and merge joined. BHF93] uses a technique based on grid files. Gun93] was the first proposal of an algorithm called Synchronized Tree Traversal (STT) which adapts to a large family of spatial predicates and tree structures. The STT algorithm of [BKS93] is the most popular one because of its efficiency. Proposed ....

L. Becker, K. Hinrichs, and U. Finke. A New Algorithm for Computing Joins with Grid Files. In Proc. IEEE Intl. Conf. on Data Engineering (ICDE), 1993.

....[LR94, LR95] have focused on the case where one or both of the input relations to the spatial join do not have an index available. Recently, two join algorithms based on spatial hashing [LR96, PD96] have been proposed for the spatial join. Other approaches to this problem are presented in [BHF93, KS97, Rot91] In this paper, we focus on the case in which neither of the inputs to the join is indexed. We present a promising new algorithm, called Scalable Sweep based Spatial Join (SSSJ) It uses the distributionsweeping paradigm recently proposed in computational geometry [APR 98, ....

....reports that the performance of the resulting algorithm is sensitive to the size of the pixels chosen. Choosing smaller pixels leads to better filtering, but increases the space needed, since the spatial objects get duplicated and stored in several pixels. In another transformational approach [BHF93] the MBRs of spatial objects (which are rectangles in two dimensions) are transformed into points in higher dimensions. The resulting points are stored in a multi attribute data structure such as the grid file [NHS84] The filtering step is then performed with the data structure. Rotem [Rot91] ....

L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In International Conference on Data Engineering, pages 190--198, Los Alamitos, Ca., USA, April 1993. IEEE Computer Society Press.

....the disk blocks in terms of the number of records that they can hold. 3 Several alternative organizations for the grid file directory control its growth and make it proportional to the data size. These alternative organizations include the region representation directory and the BR 2 directory [3]. The 2 level directory organization [20] shows how to implement the directory on disk. We have not yet explored how these techniques would work in our environment. Policy Splitting dimension DB always Database Word always Word Bounded If DB splits bound then Database else Word ....

....queries, where the queries involve disjunction as well as conjunction. There is more work to be done on the storage of these summaries as well. An unfortunate aspect of the grid files is their need for a relatively large directory. Techniques have been reported for controlling directory size [3]; we must examine whether those techniques are applicable to the highly skewed grid files generated by the GlOSS summaries. Compression techniques [41] would have a significant impact on the performance figures reported here. Finally, building an operational GlOSS server for a large number of ....

Ludger Becker, Klaus Hinrichs, and Ulrich Finke. A new algorithm for computing joins with grid files. In Proceedings of the 9 th International Conference on Data Engineering, pages 190--197, 1993.

....Numerous algorithms have been proposed to execute the filter step of a spatial join. Many of the earlier algorithms are based on transforming an approximation of a spatial object into another domain (e.g. a 1 dimensional domain) and performing the filter step in the newdomain[OM88,Ore86,BHF93] The drawback of this approach is that in the new domain some spatial proximity information is lost, making the algorithms complex and less efficient. Most of the newer algorithms are based on using spatial indices for performing the filter step of the spatial join [BKS93, G un93, HS95] and ....

....for building the spatial join index requires grid files for indexing the spatial data, and uses these grid files to compute the spatial join index. Grid files [NHS84] and kd trees [Ben75, Ben79] have also been employed for evaluating multi attribute joins in the relational domain [KHT89, HNKT90, BHF93] These methods can also be used for evaluating the filter step by storing the bounding box of the spatial objects as points in a higher dimension [BHF93] Recently, spatial index structures like R trees [Gut84] R trees [CFR87] R trees [BKSS90] and PMR quad trees [NS86] have been used to ....

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L. Becker, K. Hinrichs, and U. Finke. "A New Algorithm for Computing Joins With Grid Files". In IEEE Transactions on Knowledge and Data Engineering, 1993.

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L. Becker, K. Hinrichs, and U. Finke. A new algorithm for computing joins with grid files. In Proceedingsof the 9th IEEE International Conference on Data Engineering, pages 190-- 197, Vienna, Austria, April 1993.

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