T. K. Sellis, N. Roussopoulos and C. Faloutsos, "The R+-Tree: A Dynamic Index for Multi-dimensional Objects", Proc. of VLDB, pp. 507-518, 1987.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....helps to reduce overlaps. Note that the result of a box when some areas are subtracted from it may be a set of boxes rather than a single box. So an object to be inserted may be fragmented into several smaller boxes by this optimization. One choice to handle this is to follow the R tree ([SRF87]) approach, i.e. to insert every small box as a separate copy. But this choice increases the space overhead. Another choice is to maintain the list of small boxes in the execution of the insertion algorithm. As we go down the tree, some small boxes may become smaller or obsolete. Eventually at the ....

T. K. Sellis, N. Roussopoulos and C. Faloutsos, "The R+-Tree: A Dynamic Index for Multi-dimensional Objects", Proc. of VLDB, pp. 507-518, 1987.

....subtrees that are rooted in inner nodes. C A B N M L H D F E G K J I D E F G H I J K L MN A B C ae ae ae ae= C C CW Q Q Q Q Qs Fig. 1. An example of an R tree Many variations of R trees have appeared. The most important of theses are packed R trees [18] R trees [22] and R trees [2] The R tree does not have the limitation for the number of pairs of each node and follows a node split technique that is more sophisticated than that of the simple R tree. It is considered the most efficient variant of the R tree family and, as far as searches are concerned, it ....

T. Sellis, N. Roussopoulos and C. Faloutsos: "The R+tree - a Dynamic Index for Multi-Dimensional Objects", Proceedings of the 13th VLDB conference, 1987, pp. 507-518.

....building algorithm BuildIndex. Dual Match has additional advantages: 1) it can use point access methods (PAMs) as the index, and 2) the index creation is very fast. Multidimensional index methods can be categorized into PAMs [13, 14, 16, 17] that store points and spatial access methods (SAMs) [3, 9, 15] that store spatial objects [8] Since Dual Match stores points, it can use a PAM as the index with a flexibility of using various multidimensional indexes of differing characteristics. Dual Match can create the index much faster than FRM, since it needs only 1= as many calls as in FRM to feature ....

Sellis, T., Roussopoulos, N., and Faloutsos, C., "The R + -tree: A Dynamic Index for Multidimensional Objects," In Proc. the 15th Int'l Conf. on Very Large Data Bases, Brighton, England, pp. 507-518, Sept. 1987.

....particularly suitable for indexing features because they are designed for one dimensional vectors, but not multi dimensional vectors like the ones used in databases. Therefore, people have begun to develop new indexing methods for content based retrieval in databases such as R tree [33] R tree [63], R tree [6] SR tree [39] Quad tree [21] k d tree [7] VP tree [71] MVP tree [9] and some other methods [8, 68] 4 Chapter 1 Introduction 1.2 Problem Defined Generally, multimedia databases contain database objects with features approximately in Gaussian distributions and there usually ....

....or more minimum bounding rectangles. All the involved rectangles have to be examined to find out the results of the query which lessen the efficiency of the retrieval. Therefore, it is better to decrease the overlapping area as much as possible so as to make the retrieval faster. R tree R tree [63] is a variation of R tree. Unlike R tree, its searching and updating algorithms are modified in order to avoid the overlapping rectangles in the intermediate nodes of the indexing tree. According to the experimental results in [63] R tree has a better searching performance than R tree. Also, it ....

[Article contains additional citation context not shown here]

T. Sellis, N. Roussopoulos, and C. Faloutsos. "The R + -tree: a dynamic index for multidimensional objects". In Proceedings of the 13th VLDB Conference, pages 507--518, 1987.

....dimension assignments and also introduce optimized algorithms for query processing using striped trees. Note that tree striping as defined so far is independent of the multidimensional index structure used. Any multidimensional index structure such as the R tree [7] and its variants (R tree [17], R tree [2] P tree [9] Buddy tree [16] linear quadtrees [6] z ordering [14] or other space filling curves [8] and gridfile based methods [13, 5] may be used for this purpose. Before we describe our theoretical model, we first provide a simple algorithm for processing queries using ....

Sellis T., Roussopoulos N., Faloutsos C.: `The R+-Tree: A Dynamic Index for Multi-Dimensional Objects', Proc. 13th Int. Conf. on Very Large Databases, Brighton, England, 1987, pp. 507-518.

....with hierarchical tree structures. Use of hierarchical data structures provides higher level of information and leads to computationally less expensive management of large datasets. Sorting data according to their spatial occupancy through tree structures is a promising data manipulation scheme [13, 14]. Topological spatial relations support spatial analysis with focus on relations in a higher information level where further processing is accommodated. According to the octree structure, decomposition of data volume is performed iteratively in a step by step fashion by dividing the space into ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R+-tree: A dynamic index for multi-dimensional objects", Proceedings of the thirteenth International Conference on VLDB '87, Brighton, England, 1987, pp. 507-518.

....improved by using appropriate indexing mechanisms that support nearest neighbor search over multidimensional feature vectors. Several indexing mechanism suited for multimedia features (referred to as the F index or the feature index [15] have been proposed recently (e.g. R trees [22] R trees [41], R trees [2] k d B trees [34] hB trees [11] TV trees [27] SS trees [52] vp trees [8] M trees [9] Any such indexing mechanism can be used for indexing the feature vectors. We have developed a hybrid multidimenional index mechanism that combines the advantages of the two broad classes of ....

 T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R+-Tree: A Dynamic Index for Multi-Dimensional Objects," Proc. 12th VLDB, 1987.

....the amount of memory required to hold such information could be large for indices with high fan out, such as R trees. Analytical models were to used to study the performance of various techniques, but memory constraints were not considered in depth. The R tree and its variations [12] 13] 14] [15] have been gaining popularity due to their relatively simple structure and their efficient handling of spatial objects with extent, such as region objects. An R tree is a B tree like access method that stores multidimensional spatial objects. An internal R tree node contains entries of the ....

....a data set that is the output of an earlier spatial or non spatial operation a derived data set. Our approach to supporting such queries is to dynamically build access methods for the derived data sets as necessary to support spatial join. However, most spatial access methods [12] 13] 14] [15] were originally designed for a different context. In particular, such indices are assumed to be built up incrementally, and are not optimized for all at once construction. Most such indices are also designed to minimize the cost of spatial selection, not that of spatial join. They try to reduce ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R + - tree: A dynamic index for multi-dimensional objects," in Proceedings of Very Large Data Bases, pp. 3--11, Brighton, England, 1987.

....databases where sequences are of different lengths. 1 The time warping distance is widely used in such applications as voice recognition [20] and electro cardiogram analysis. For efficient processing of similarity search, most of previous approaches [1, 2, 11] employ multidimensional indexes [3, 5, 22]. Yi et al. 25] claimed that the multi dimensional indexes assuming the triangular inequality [19] directly or indirectly cause false dismissal in similarity search when their distance functions do not satisfy the triangular inequality. False dismissal [1, 11] is to miss part of the final query ....

....searching method. 4.3.1 Index Construction Each data sequence is mapped to a point in 4 dimensional space since a 4 tuple feature vector is extracted from a sequence for indexing. For indexing a set of 4 dimensional points, any multidimensional indexes such as the R tree [13] R tree [22], R tree [3] and X tree [5] can be used. The index construction algorithm first makes an entry h F irst(S) Last(S) Greatest(S) Smallest(S) ID(S) i for each data sequence S and then inserts it into a multi dimensional index. Here, ID(S) is the identifier of S. If there are a large number of ....

T. K. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -Tree: A Dynamic Index for MultiDimensional Objects", Proc. VLDB , pp. 507-518, 1987.

....complex rewriting to GRA expressions. ffl Indexing data structures. The presence of set selection operators in EGRA requires the use of index structures to support both containment and intersection queries. Spatial data structures with good average bounds, such as R trees and their variants [19] [35], can be used for those purposes. However, other data structures having good worst case complexity and scaling well to high dimensions have to be developed. See [7] for some preliminary results. 2. More general issues. ffl Canonical forms. In order to efficiently perform algebraic operations and ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R + -tree: A Dynamic Index for Multi-Dimensional Objects," in Proc. of the 13th Int. Conf. on Very Large Data Bases, 1987, pp. 507--518.

....index structures, and briefly review the previous work. In section 3.3, vp tree structure is discussed in more detail. 3. 1 Distance Transformations to Euclidean Spaces For low dimensional Euclidean domains, the conventional index structures ( Sam89] such as R trees (and its variations) [Gut84, SRF87, BKSS90] can be used effectively to answer similarity queries. In such cases, a near neighbor search query would ask for all the objects in (or that intersects) a spherical search window where the center is the query object and the radius is the tolerance factor r. There are some special techniques for ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R+-tree: A Dynamic Index for Multi-dimensional Objects", Proceedings of the 13 th VLDB Conference, pages 507-518, September 1987.

.... proximity by recursively dividing the space, using a splitting rule to construct a grid or a hierarchy of regions [17] A survey of these methods can be found in [34] Some of the representative Isotropic Access Methods (ISM s) include grid files [31] cell trees [17] R trees [18] and R trees [36]. Isotropic spatial access methods have traditionally been used to store vector spatial data such as sets of polygons, and they allow flexible policies which can be adapted to take advantage of connectivity information. The literature on transitive closure and recursive query processing has ....

....the Grid file [31] the Cell Tree [17] Zordering [32] and DFS AM [5, 28] CCAM S denotes the static create operation of CCAM. CCAM D is an incremental create( operation which was implemented using the second order reorganization policy. The Celltree represents the family containing R tree [36]. The Grid file and the Cell tree partition the space to capture the isotropic nature of spatial proximity, which is an important property of spatial networks. We consider two versions of the Grid file and Cell tree, including connectivity based and balance based split policies, as described in ....

T. Sellis, N. Roussopoulos, and C. Faloutsos. "The R + -Tree: A Dynamic Index for Multi-Dimensional Objects". In Proc.13th Intl Conference on Very Large Data Bases, pages 507--518, 1987.

....methods, for structural query processing. The R tree [G84] is a multidimensional extension of the height balanced B tree that stores the MBRs of the actual data objects in the leaf nodes; intermediate nodes are built by grouping rectangles at the lower level. Several variations of R trees (e.g. [SRF87] [BKSS90] have been proposed to enhance the performance of the original structure. Traditionally R trees have been used for window queries, i.e. queries that return all objects overlapping a reference window. Other types of retrieval such as direction and topological queries can be transformed ....

Sellis, T., N. Roussopoulos, and C. Faloutsos "The R+ -Tree: A Dynamic Index for Multi-Dimensional Objects". VLDB, 1987.

....indexing structure of the underlying feature vectors support an efficient and effective retrieval of user queries. Recently, researchers havedeveloped many new indexing methods for contentbased retrieval in multimedia databases. For example, rectangle based indexing as in R Tree [6] R Tree [11], R Tree [1] SR Tree [7] Partition based Indexing as in Quad tree [5] k d Tree [2] VP Tree [4, 13] and MVP tree [3] However, one major problem of these indexing techniques has been that these methods fail to utilize the underlying data distribution to their advantage in their indexing ....

T. Sellis, N. Roussopoulos, and C. Faloutsos. "The R + -tree: a dynamic index for multidimensional objects". In Proceedings of the 13th VLDB Conference, pages 507--518, 1987.

....higher than three. k d tree based nearest neighbor algorithms have been widely used in computer vision [2, 42] k d trees are extremely versatile and efficient to use in low dimensional cases. However, the performance degrades exponentially in high dimensional cases. R tree and its variants [22, 34, 1] have similar performance of nearest neighbor searches in high dimensions. In [14] we present an efficient algorithm which uses a hierarchical quasi Voronoi diagram to search for the nearest neighbor. Table 2 shows average computation time for each sequence on the SGI INDIGO 2. The time was ....

T. Sellis, N. Roussopoulos and C. Faloutsos, "The r+-tree: a dynamic index for multidimensional objects", in Proceedings of 13th International Conference on VLDB, pp. 507-518, 1987.

....with dimensionality higher than three. k d tree based nearest neighbor algorithms have been widely used in computer vision [2, 35] k d trees are extremely versatile and efficient to use in low dimensions. However, the performance degrades exponentially in high dimensions. R tree and its variants [1, 17, 28] have similar performance of nearest neighbor searches in high dimensions. Yianilos presented a nearest neighbor query algorithm using the vantage point tree [34] The algorithm achieves O(log n) expected time complexity under the assumption that the training samples have zero probability ....

T. Sellis, N. Roussopoulos and C. Faloutsos, "The r+-tree: a dynamic index for multidimensional objects", in Proceedings of 13th International Conference on VLDB, pp. 507-518, 1987.

....that are similar to the query sequence. However, traditional database indexing techniques are inadequate for this purpose. There is currently much excellent work in indexing multidimensional data, including multidimensional hashing, grid based index structures[18] and the R tree family[12, 19, 11] index structures. These spatial access methods, however, are designed to index unsequenced spatial objects. The order among the entities in the database is not taken into consideration when the index structures are created and hence no e#ective retrieval method in terms of subsequence matching of ....

....called forced reinsert: when a node overflows, it is not split right away, but a portion of the entries are removed and reinserted into the tree. The R # tree also refines the node splitting policy of the R tree by taking overlapping area and region perimeter into consideration. The R tree[19] imposes the constraint that no bounding rectangles of non leaf nodes can overlap. Thus, point searches in the R tree correspond to a single path traversal from the root to one of the leaves. The negative impact of this constraint is that no minimum space utilization can be guaranteed and the ....

T. Sellis, N. Roussopoulos, C. Faloutsos: "The R + -tree: a dynamic index for multidimensional objects." In Proc. 13th International Conference on VLDB, pp. 507-518, England, 1987.

...., this paper, we focus on access methods that manage the secondary storage pages by rectilinear hyperrectangles, e.g. minimum bounding rectangles (MBRs) for forming higher level directory pages. For instance, this paradigm is realized in the R tree [Gut 84] and its derivatives, R tree [SRF 87] R tree [BKSS 90] as well as in the X tree [BKK 96] which has already been used successfully to support query processing for dimensionalities up to 16. Up to now, similarity query processing using PAMs and SAMs supports only the Euclidean distance where query ranges are spherical, and ....

Sellis T., Roussopoulos N., Faloutsos C.: `The R+-Tree: A Dynamic Index for Multi-Dimensional Objects', Proc. 13th Int. Conf. on Very Large Databases, Brighton, England, 1987, pp. 507-518.

....of space (like Quadtrees) and are suitable for indexing multi dimensional points and line segments. The nodes of these structures coincide to disk pages and the leaf nodes all appear at the same level (like R trees [4] The regions to which space is partitioned are disjoint (like R trees [8]) These structures are called External Balanced Regular (x BR) Trees and are fully dynamic, while insertions are not complicated to program and affect only one path in the tree (in contrast to R trees) Moreover, x BR trees are variable resolution structures. That is, the number of space ....

T. Sellis, N. Roussopoulos and C. Faloutsos: "The R+tree - a Dynamic Index for MultiDimensional Objects", Proceedings 13th VLDB Conference, pp.507-518, 1987.

....for 2 dimensional range searching and its special cases (see [7] for a detailed survey) Most of these algorithms are not efficient when mapped to secondary storage. However, the practical need for good I O support has led to the development of a large number of empirical external data structures[15,16,21,23,24,28,29,30,32] which do not have good theoretical worst case bounds but have good average case behavior for common spatial database problems. The worst case performance of these data structures is much worse than the optimal bounds achievable for dynamic external 1 dimensional range searching using B ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R + -Tree: A Dynamic Index for Multi-Dimensional Objects," Proc. 1987 VLDB Conference, Brighton, England (1987).

....tourist authorities for advertising purposes. The value of K is dependent on the advertising budget of the tourist authorities. The fundamental assumption is that the two spatial data sets are stored in structures belonging in the family of R trees [12] R trees and their variants (R trees [26], R trees [2] etc) are considered an excellent choice for indexing various kinds of spatial data (like points, polygons, 2 d objects, etc) and have already been adopted in commercial systems (Informix, Oracle, etc) In this paper we focus on sets of point data. Five di#erent algorithms are ....

T. Sellis, N. Roussopoulos and C. Faloutsos: "The R + tree - a Dynamic Index for Multi-Dimensional Objects", Proceedings 13th VLDB Conference, pp.507-518, Brighton, UK, 1987.

....on the constraint indexing technique that achieves the same bounds using a single B tree. Updates can be made to this structure, but the optimal bound obtained (O(log B n) is amortized. Orthogonal to these approaches, constraint indexing can be performed using members from the R tree family [3,9,16]. These data structures do not guarantee good worst case bounds, but have been empirically determined to provide good average performance for interval indexing and other problems. In summary, we present solutions for constraint and temporal indexing that are considerably simpler than previous ....

T. Sellis, N. Roussopoulos & C. Faloutsos, "The R + -Tree: A Dynamic Index for Multi-Dimensional Objects," Proc. 13th VLDB Conference (1987).

.... has been an active area of research over the past ten years [LT92, G94] A major component of such research efforts has been, and continues to be, concerned with the design of efficient spatial data indexing methods which reduce query response time during spatial query processing [Gut84, SRF87, HSW89, BKS90, KF94] Some promising proposals have been reported in the literature aimed at enhancing these indices with additional, specific query handling capabilities Work supported by the European Union s TMR program ( CHOROCHRONOS project, contract number ERBFMRX CT96 0056) and by the ....

T. Sellis, N. Roussopoulos and C. Faloutsos: "The R + -tree: a Dynamic Index for Multidimensional Objects", Proceedings 13th VLDB Conference, pp.507-518, Brighton, UK, 1987.

....database systems have been extensively investigated during the last decade. A great variety of index structures and query processing techniques has been proposed [G t 94, GG 98] Most techniques are based on hierarchical tree structures such as the R tree [Gut 84] and its variants [BKSS 90, SRF 87, BKK 97] In these approaches, each node corresponds to a page of the background storage and to a region of the data space. There is an increasing interest in integrating spatial data into commercial database management systems. Geographic information systems (GIS) are data intensive applications ....

Sellis T. K., Roussopoulos N., Faloutsos C.: `The R+-Tree: A Dynamic Index for MultiDimensional Objects', Proc. 13th Int. Conf. on Very Large Data Bases, Brighton, England, 1987, pp. 507-518.

....least miniconf , where fi Gamma ff is obtained by deleting the prefix ff from fi. Essentially, the discovery problem requires to index substrings together with their support and position information. Let us review several existing techniques for serving this purpose. The R tree [G84] and R tree [SRF87] support operations on multi dimensional data. They can be used for strings by treating the position as one dimension and substrings as the second dimension. However, since the number of possible substrings in a string of length n can be O(n 2 ) and a substring can be scattered all over the ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R+-tree: A dynamic index for multidimensional objects", VLDB 1987, 507-518

....Simple top down graph traversal algorithms can be used to achieve search pruning at all levels. In [3] search pruning is done by synchronously traversing the two input R trees depth first 3 In most R trees variances [2, 7, 5] partitions at each level may overlap. An exception is R tree [17], for which partitions at each level do not overlap. BFRJ is independent of this variance. whereas in BFRJ it is achieved by synchronized breadth first traversal of both R trees. The effect of search pruning at all R tree levels is that, starting from the top level, the two nodes, one from each ....

Sellis, T., Roussopoulos, N. and Faloutsos, C., "The R + -Tree: A Dynamic Index for Multidimensional Objects," Proc. of the VLDB Conf., Brighton, England, 1987, pp. 3 -- 17.

....searching demands that both overlap and coverage be minimized. Zero overlap is in general not attainable for region data objects. However, if we allow partitions to split rectangles then zero overlap among intermediate node entries can be achieved. This is the main idea behind the R tree [SELL87]. Finally, the R tree [BECK90] is a variation of the R tree which unlike the R tree does not change the properties of the structure, but rather has a more complex way to organize rectangles into nodes so that overall performance is improved. 2. Optimization of Tree Performance When ....

....the group with the largest size and the most members. b) If one group has so few entries that all the rest must be assigned to it, the assignment is done without any control. R tree: Because of the disjointness property of the method, downward propagation of the split may be necessary [SELL87]. R tree: The algorithm uses two kinds of criteria: the margin criterion to select a split axis and the overlap criterion to select a distribution along the split axis. This separation may cause the loss of a good distribution if that latter one belongs to the axis that has been rejected. In ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: a dynamic index for multidimensional objects", Proc. 13th VLDB Conf., 1987, pp. 507-518.

....inserting one object at a time as specified by Guttman has several disadvantages: a) high load time, b) sub optimal space utilization, and, most important, c) poor R tree structure requiring the retrieval of an unduly large number of nodes in order to satisfy a query. Other dynamic algorithms [1, 13] improve the quality of the R tree, but still are not competitive with regard to query time when compared to loading algorithms that are allowed to preprocess the data to be stored. Preprocessing is particularly reasonable for applications where the data is fairly static (i.e. does not change ....

Sellis, T., Roussopoulos, N., Faloutsos, C., "The R+ Tree: A Dynamic Index for Multidimensional Objects, " Proc. 13th International Conference on Very Large Databases (VLDB-87), p. 507-518, September

....[Peuq87, Muke90] Then we show how the relations that we define can be efficiently retrieved in existing DBMSs. Although for other types of spatial relations, such as topological relations, there has been extensive work in spatial data structures and specialised indexing methods have been proposed [Gutt84, Sell87, Beck90, Papa95b], limited work has focused on direction relations (see [Papa94b] for related work) The results of this paper are directly applicable to Spatial Databases and Geographic Information Systems (GISs) where the formalization of spatial relations is crucial for user interfaces and query optimisation ....

....by grouping rectangles at the lower level. An intermediate node is associated with some rectangle which encloses all rectangles that correspond to lower level nodes. The fact that R trees permit overlap among node entries sometimes leads to unsuccessful hits on the tree structure. The R tree [Sell87] and the R tree [Beck90] methods have been proposed to address the problem of performance degradation caused by the overlapping regions or excessive dead space respectively. In this paper we use R trees because we found them to have consistently better performance in the retrieval of ....

Sellis, T., Roussopoulos, N., Faloutsos, C., "The R + -tree: A Dynamic Index for Multi-Dimensional Objects", In the Proceedings of the 13th Very Large Data Bases Conference, 1987.

....and attempt to capture their particular properties concerning evaluation criteria outlined in Section 2.1. Table 1. Classification of decomposition techniques Strategy Properties of Decomposition Indexing Structures Condition Number Containers No no redundancy 1 MBR R tree[10] R tree[11] R tree[12] Reqular regular grid 2 d a set of fixed grids quad tree[13] B tree with z value[7] Variable Grid grid and object shape variable variable cells edge quadtree[14] PM quadtree[14] Structural object structure n MBRs Cell tree[15] TR tree[16] Controlled controllable parameters ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R + -tree: A Dynamic Index for Multi-dimensional Objects," Proc. 13th Very Large Data Bases, Conf. Sep. 1987, pp. 507-518.

....an object may be covered by more than one rectangle. Thus, it may be necessary to search multiple subtrees to find the desired object. Two variants of the R tree, the R tree and the R tree, were developed to improve performance by minimizing and eliminating overlapping regions. R trees [3] improve performance by eliminating overlap. That is, non leaf nodes may not have rectangles which overlap. This adds additional complexity to the insertion, deletion and node splitting operations and tends to make the tree higher (more levels) But the extra time for these operations is offset by ....

....Merging reinserting entries is not done in our implementation of R trees for two reasons: First since by definition, the covers of sibling nodes may not overlap, a reinsertion of an orphaned entry will end up in the same place in the tree as it originally was. Second, the description of R trees [3] was not clear about how to handle underpopulated nodes. We chose not to do anything for underpopulated nodes. We felt that we didn t do enough deletes in our test cases to cause a significant degradation in performance due to underpopulated nodes. 3.3. Encountered Problems The R split algorithm ....

[Article contains additional citation context not shown here]

Sellis, T., Roussopoulos, N., and Faloutsos, C. "The R+-Tree: A Dynamic Index for Multi-Dimensional Objects", Proc. 13th Conf. Very Large Data Bases, Brighton, 1987, pp. 507-518.

....index structures, and briefly review the previous work. In section 3.3, vp tree structure is discussed in more detail. 3. 1 Distance Transformations to Euclidean Spaces For low dimensional Euclidean domains, the conventional index structures ( Sam89] such as R trees (and its variations) [Gut84, SRF87, BKSS90] can be used effectively to answer similarity queries. In such cases, a near neighbor search query would ask for all the objects in (or that intersects) a spherical search window where the center is the query object and the radius is the tolerance factor r. There are some special techniques for ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R+-tree: A Dynamic Index for Multi-dimensional Objects", Proceedings of the 13 th VLDB Conference, pages 507-518, September 1987.

....used in spatial and scientific databases. By storing the bounding boxes of arbitrary geometric objects, such as points, polygons, or more complex objects, R trees can be used to determine which objects intersect a given query region. Several variants have been proposed to improve performance [1, 5, 9]. Performance studies of various R tree algorithms, have used the number of nodes accessed as the primary metric. In real databases some portion of the tree is buffered in main memory. Since such buffering can significantly affect performance, we postulate that performance prediction should be ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R+ Tree: A Dynamic Index for Multidimensional Objects", Proc. 13th International Conference on Very Large Databases (VLDB-87), p. 507-518, September 1987.

....bounding rectangles of the subtrees that are rooted in inner nodes. C A B N M L H D F E G K J I DE F G H I J K LMN A B C ae ae ae ae= C C CW Q Q Q Q Qs Figure 1: An example of an R tree Many variations of R trees have appeared. The most important of theses are packed R trees [18] R trees [22] and R trees [2] The R tree does not have the limitation for the number of pairs of each node and follows a node split technique that is more sophisticated than that of the simple R tree. It is considered the most efficient variant of the R tree family and, as far as searches are concerned, it ....

T. Sellis, N. Roussopoulos and C. Faloutsos: "The R+tree - a Dynamic Index for MultiDimensional Objects", Proceedings 13th VLDB conference, pp.507-518, 1987.

.... the following features[7] 8] 1) spatial data types for representation of commonly occurring geometric information such as point, line, and polygon; 2) generic spatial operators (such as such as overlap and intersect) among these types; 3) spatial indexes like R tree[9] R tree[10] R tree[11]. These spatial features are best implemented in object oriented database systems because many possible domain specific spatial types can be derived from a set of basic ones through the type inheritance mechanism. Implementation of spatial operators may be encapsulated as methods within the object ....

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R+-tree: A dynamic index for multi-dimensional objects," In Proc. of the 13th VLDB Conf., 1987, pp. 507-518.

....multiple attribute data in a more direct manner. The above access techniques specialize in efficient access to spatial point data and require spatial transformations to search multi dimensional spatial data relevant to our work. R trees [9] however are designed for such multi dimensional data. In [3, 21], different variations of the R tree are presented. In our experiments, we deploy an R tree based on [9] but with input data properly packed by their spatial proximity. For spatial join, 4, 8, 13, 14, 18, 19] proposed various techniques. Among them, we use the optimization techniques proposed in ....

Sellis, T., Roussopoulos, N. and Faloutsos, C., "The R + -Tree: A Dynamic Index for Multidimensional Objects," Proc. of the VLDB Conf., Brighton, England, 1987, pp. 3 -- 17.

....large sets of multi dimensional (spatial) data, such as points or regions, is of crucial importance in several applications, including Spatial, Image or Multimedia Database Systems. In recent years, several data structures have been developed for point [Niev84, Free87, Henr89] and non point [Gutt84, Sell87, Gunt89, Beck90] spatial objects. All these indexing methods use several heuristics to index spatial data efficiently. The large number of spatial data structures proposed indicate that, today, research in this field should turn to the development of powerful analytical models that predict the performance of a ....

....index will have on the performance of answering a query. Some efforts towards the analytical estimation of the performance of spatial data structures have been presented in the past. Faloutsos et al. Falo87] presented a model that estimates the performance of R trees [Gutt84] and R trees [Sell87] assuming uniform distribution of data and packed trees (i.e. all the nodes of the tree are full of data) Recently, Kamel and Faloutsos [Kame93] and Pagel et al. Page93] independently presented a formula that gives the average number of disk accesses in an R tree index accessed by a query, ....

[Article contains additional citation context not shown here]

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: a dynamic index for multidimensional objects", Proceedings of the 13th VLDB Conference, 1987.

....essential information for the construction of a spatial index. The most commonly used abstraction of complex spatial objects, which is considered in this paper, is the Minimum Bounding Rectangle (MBR) Existing SAMs may be classified into four groups based on the technique used for managing MBRs [Sell87, Seeg88, Smit90]: a) Ordering, b) Clipping, c) Overlapping, and d) Transformation. The purpose of this paper is to introduce a new technique for SAMs, termed Abstraction. Section 2 briefly reviews existing SAMs organizing MBRs and classifies them according to the technique they adopt. Section 3 describes the new ....

.... 1 i=1 so that each R i , 1 i k, intersects with exactly one disjoint region. These rectangles are represented in a file and may be organized by any multidimensional PAM, like the grid file [Niev84] or the K DB tree [Robi81] Examples of SAMs using the clipping technique are the R tree [Sell87] and the Cell tree [Gunt89] Since these structures avoid overlapping regions the search operation is very efficient. Additionally, the properties of the underlying PAM are inherited. However, a drawback is obviously the significant data replication, which increases the index size and degrades the ....

T. Sellis, N. Roussopoulos, C. Faloutsos: `The R + -tree: A Dynamic Index for MultiDimensional Objects', Proceedings of the 13th VLDB Conference, Brighton, England, 507-518, 1987.

....temporal characteristics (duration and start stop time) of the objects. In the literature concerning the area of spatial databases, several data structures have been proposed for the manipulation of spatial data (a survey can be found in [Same89] Among others, R trees [Gutt84] and their variants [Sell87, Beck90] seem to be the most efficient ones. On the other hand, the manipulation of temporal information can be supported either by one dimensional versions of the above data structures (since all of them have been designed for n dimensional space in general) or by specialised temporal data structures, ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: A Dynamic Index for Multidimensional Objects", Proceedings of the 13th International Conference on Very Large Databases (VLDB), 1987.

....large sets of multi dimensional (spatial) data, such as points or regions, is of crucial importance in several applications, including Spatial, Image and Multimedia Database Systems. In recent years, several data structures have been developed for point [NHS84, Fre87, HSW89] and non point [Gut84, SRF87, BKSS90, KF94] objects in multi dimensional space. All these indexing methods use several heuristics to index spatial data efficiently. The large number of spatial data structures proposed indicate that, today, research in this field should turn to the development of powerful analytical models that predict the ....

....R tree After Guttman s proposal, several researchers proposed their own improvements on the basic idea. Among others, Roussopoulos and Leifker [RL85] proposed the packed R tree, for the case that data objects are known in advance (i.e. it is applicable only to static databases) Sellis et al. [SRF87] proposed the R tree, a variant of R trees that guarantees disjointness of nodes, Beckmann et al. BKSS90] proposed the R tree, an R tree based method that uses a rather complex but effective grouping algorithm, Kamel and Faloutsos [KF94] proposed the Hilbert R tree, an improved R tree ....

[Article contains additional citation context not shown here]

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: a dynamic index for multidimensional objects", In Proceedings of the 13th International Conference on Very Large Data Bases (VLDB), September 1987.

....large sets of multi dimensional (spatial) data, such as points or regions, is of crucial importance in several applications, including Spatial, Image or Multimedia Database Systems. In recent years, several data structures have been developed for point [Niev84, Free87, Henr89] and non point [Gutt84, Sell87, Beck90] objects in multidimensional space. All these indexing methods use several heuristics to index spatial data efficiently. The large number of spatial data structures proposed indicate that, today, research in this field should turn to the development of powerful analytical models that predict the ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: a dynamic index for multidimensional objects", Proceedings of the 13th VLDB Conference, 1987.

....and dead space in the nodes, which in turn results to bad performance. A packing technique proposed in [ROUS85] alleviates this problem for relatively static databases of points. However, for update intensive spatial databases, packing cannot be applied on every single insertion. The R tree [SELL87] and the R tree [BECK90] methods have been proposed to address the problem of performance degradation caused by the 5 overlapping regions or excessive dead space respectively. However, all of the above methods try to address the problem in a rather ad hoc way. In a later section we propose a ....

....If one group has so few entries that all the rest must be assigned to it, the assignment is done without any control. This fact, usually, causes high overlap between the two nodes. R tree . Because of the disjointness property of the method, downward propagation of the split may be necessary [SELL87]. The most important problem is that a dead lock is possible because it is not certain that a partition line will be always found. For example, if each of the rectangles in the node overlaps all others then a partition is not possible. R tree . The algorithm uses two kinds of criteria: the ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: a dynamic index for multidimensional objects", Proc. 13th VLDB Conf., 1987, pp. 507-518.

....by grouping rectangles at the lower level. An intermediate node is associated with some rectangle which encloses all rectangles that correspond to lower level nodes. The fact that R trees permit overlap among node entries sometimes leads to unsuccessful hits on the tree structure. The R tree [Sell87] and the R tree [Beck90] methods have been proposed to address the problem of performance degradation caused by the overlapping regions or excessive dead space respectively. In order to retrieve objects that satisfy a direction relation with respect to a reference object we have to specify ....

Sellis, T., Roussopoulos, N., Faloutsos, C., "The R + -tree: A Dynamic Index for Multi-Dimensional Objects", Proceedings of the 13th International Conference on Very Large Data Bases (VLDB), 1987.

....of the NN location. Then it backtracks and explores remaining subtrees which potentially contain NN until no subtree needs be visited. In [FBF77] a NN algorithm for k d trees was proposed which was later refined in [Spro91] R trees [Gutt84] Packed R trees [Rous85] Kamel93] R tree variations [SRF87], Beck90] have been primarily used for overlap containment range queries and spatial join queries [BKS93] based on overlap containment. In this paper, we provide an efficient branch and bound search algorithm for processing exact k NN queries for the R trees, introduce several metrics for ....

Sellis T., Roussopoulos, N., and Faloutsos, C., "The R+-tree: A Dynamic Index for Multidimensional Objects," Proc. 13th International Conference on Very Large Data Bases, 1987, pp. 507-518.

....presents the conclusions and future research directions. 2. Survey The problem is to store and retrieve spatial objects on secondary store (disk) As mentioned before, a general object is represented by its minimum enclosing rectangle. Access methods for such rectangles form three classes [18] [19]. We examine the first two in more detail, because they are necessary to describe the proposed DOT method. Class 1: Methods that transform the rectangles into points in a space of higher dimensionality [9] For example, a 2 d rectangle with sides parallel to the axes is characterized by four ....

....Shuffling function: the point (x 1 x 2 , y 1 y 2 ) gives (x 1 y 1 x 2 y 2 ) Class 3: Methods that divide the original space into appropriate sub regions. The sub regions may be overlapping, such as in R trees [7] 16] or they may be disjoint, such as in the cell trees [6] or in the R trees [19]. 3. Proposed approach The proposed method suggests pipelining the transformations of Class 1 and Class 2 of the survey section. The resulting method enjoys the best of both worlds, avoiding the drawbacks of its individual transformation: # like the z ordering of Class 2, it can be easily ....

[Article contains additional citation context not shown here]

Sellis, T., N. Roussopoulos, and C. Faloutsos, "The R+ Tree: A Dynamic Index for MultiDimensional Objects," Proc. 13th International Conference on VLDB, pp. 507-518, England,, Sept. 1987. also available as SRC-TR-87-32, UMIACS-TR-87-3, CS-TR-1795

....objects, and . a temporal index for the temporal characteristics (duration and start stop time) of the objects. In the literature concerning the area of spatial databases, several data structures have been proposed for the manipulation of spatial data. Among others, R trees [7] and their variants [1, 11] seem to be the most efficient ones. On the other hand, the manipulation of temporal information can be supported either by one dimensional versions of the above data structures (since all of them have been designed for n dimensional space in general) or by specialized temporal data structures. ....

T. Sellis, N. Roussopoulos, C. Faloutsos, "The R + -tree: A Dynamic Index for Multidimensional Objects", Proceedings of the 13th International Conference on Very Large Databases (VLDB), September 1987.

No context found.

Sellis, T., Roussopoulos, N. and Faloutsos, C., "The R + -Tree: A Dynamic Index for Multi-dimensional Objects," Proc. of the VLDB Conf., Brighton, England, 1987, pp. 3 -- 17.

No context found.

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R + -tree: A dynamic index for multidimensional objects ", Proc. 13th VLDB Conf., pp. 507--518 (1987).

No context found.

Sellis, T., Roussopoulos, N., Faloutsos, C., "The R+ Tree: A Dynamic Index for Multi-Dimensional Objects," Proc. 13th Inf. Conf. on VLDB, 1987, pp. 507-518.

No context found.

T. Sellis, N. Roussopoulos, and C. Faloutsos, "The R + tree: A dynamic index for multidimensional objects," Proc. Int. Conf. on Very Large Data Bases , pp. 507--518, 1987.

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