Faloutsos C., Roseman S. "Fractals for Secondary Key Retrieval." Proceedings of the Eighth ACM SIGACT-SIGMID-SIGART Symposium on Principles of Database Systems (PODS). 1989  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and the size of the query objects. 1. Introduction There is a growing demand for database applications to handle intervals which, for instance, occur as transaction time and valid time ranges in temporal databases [31] 26] 4] or as line segments on a space filling curve in spatial applications [9] [3] The SQL:1999 standard provides the datatype PERIOD with the predicates precedes, succeedes, meets, equals, overlaps ( intersects) contains, and during [30] With the Relational Interval Tree (RI tree) a relational access method has been proposed which supports all of the PERIOD ....

Faloutsos C., Roseman S.: Fractals for Secondary Key Retrieval. Proc. ACM PODS, 247-252, 1989.

....space filling curves have shown to be of high value [2] 4] 9] 11] 17] 20] In this paper we study Hilbert curves [10] perhaps the most popular space filling indexing schemes. Properties of two and three dimensional (2D and 3D) Hilbert curves have been extensively studied recently [5] [7], 9] 12] 14] 15] 18] However, most of the work so far has focused on empirical studies. Up to now, little attention has been paid to the theoretical study of structural properties of multidimensional Hilbert curves, the focus of this paper. Whereas with modulo symmetry there is only ....

C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In Proceedings of the 8th ACM Symposium on Principles of Database Systems, pages 27--252, 1989.

.... Piscataway, NJ 08855 1331, USA. Temporal Databases [SOL94] Quality Classes, Personalization and Fuzzy Logic Matching where intervals can be utilized to describe the problem; Spatial Data where a spatial object can be approximated by a bounding box or set of intervals on a space filling curve. FR89, BKK99, KMPS01] For point data there are only a few well defined query types, e.g. point query and range query, but for intervals there are plenty different query types, e.g. the 13 Allen Relations [AH85] for temporal data. Following [GG98] the basic query types we consider are: Exact Match ....

Christos Faloutsos and Shari Roseman. Fractals for secondary key retrieval. In Proceedings of the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, March 29-31, 1989, Philadelphia, Pennsylvania, pages 247--252. ACM Press, 1989.

....Space Filling Curves A space filling curve [60] maps n dimensional points in the box [0, 1] onto a one dimensional curve, and provides a one dimensional order to all points on this curve. The curve itself is continuous, and never crosses itself. In particular, we will employ the Hilbert curve [20,28,64]. An approximation of the 2D Hilbert curve is shown in Figure 7a. a) Hilbert Curve (b) Z order Curve Figure 7: Space filling curve approximations. Finding the quantised arc length distance s along a Hilbert curve from quantised spatial positions (x, y, z) and vice versa are relatively ....

C. Faloutsos and S. Roseman. Fractals for Secondary Key Retrieval. In Proc. 8th ACM PODS, pages 247--252, Philadelphia, PA, 1989. 4.1

....grid in a space and these numbers are then used to obtain a representative number for the spatial objects. Techniques on ordering multi dimensional objects using single dimensional values have been proposed. These include the Peano curve [18] locatiohal keys [1] Zordering [23] Hilbert curve [11], and gray ordering [10] The mapping functions used in mapping must preserve the proximity between data well enough in order to yield reasonably good spatial search. A spatial object with extent is represented by a set of numbers or one dimensional objects. These one dimensional points are ....

C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In Proc. 1989.

.... have been proposals based on this heuristic (for a survey of these and other spatial access methods, refer to [12] All the proposed index structures have the following in common: They first partition the multidimensional space with a grid, and then use a curve such as Peano Curve or Hilbert Curve[10], which visits all the points in the grid only once without crossing itself, to obtain a total ordering of the spatial objects. BODHI indexes spatial objects using one such proposal, the Hilbert R Tree (HR Tree) 20] where total ordering is achieved through Hilbert Curve for total ordering. The ....

C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In Proc. of the ACM SIGACT/ SIGMOD Symposium on Principles of Database Systems, March 1989.

....thus likely to intersect many of these directory rectangles, resulting in an excess of disc accesses [10] An improvement is described in [10] where a space filling Hilbert curve is used to sort the rectangles according to the Hilbert coordinates of their centers. It was reported in earlier work [4, 8] that the Hilbert curve compares favorably to the Gray code and Peano space filling curve regarding clustering performance. Recently, it has been proposed to use the Hilbert curve in the dynamical insertion algorithm for the R tree [11] The algorithm becomes similar to inserting in a B tree. ....

C. Faloutsos and S. Roseman: "Fractals for secondary key retrieval", Proc. ACM PODS,

.... Such queries (spatial queries) are common in applications where it is important to retrieve images based on the position and the size of individual regions or objects (e.g. CAD CAM and geographic database applications) Techniques such as the R trees [12] 9 and techniques based on fractal curves [13] can be used to resolve such queries. However, such techniques cannot index or access images by content (i.e. in terms of relationships and properties of objects) 1.4 Thesis Outline A review of related work done in the areas of Computer Vision and DataBases is presented in Chapter 2. Image ....

....it are returned. Such queries are common in applications where it is important to retrieve images based on the position and the size of individual regions or objects (e.g. CAD CAM and geographic database applications) Techniques such as the R trees [12] and techniques based on fractal curves [13] can be used to resolve such queries. There are certain application domains (e.g. medical imaging, robotics, geographic database applications etc. in which images need to be accessed by content. To our knowledge, techniques which support the indexing of images by content have not been proposed ....

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Christos Faloutsos and Shari Roseman. Fractals for Secondary Key Retrieval. Technical Report UMIACS-TR-89-47, CS-TR-2242, University of Maryland, Colledge Park, Maryland, May 1989.

....processing and with a powerful query language supporting the treatment of variable similarity criteria as well as the processing of various types of image queries. In particular, the methodology may be extended to support the processing of fuzzy queries e.g. partial match and range queries [29, 30]. In partial match queries, one or more properties of objects contained in a query image are left unspecified, in which case, these properties are allowed to take any value in a specific domain. In range queries, instead of exact values, ranges of values of one or more properties corresponding to ....

Christos Faloutsos and Shari Roseman. Fractals for Secondary Key Retrieval. Technical Report UMIACS-TR-89-47, CS-TR-2242, University of Maryland, Colledge Park, Maryland, May 1989.

....the root to one of the leaves. Range queries, on the other hand, lead to the traversal of multiple paths in both the R tree and the R tree. A typical R tree is depicted in Figure 2.5. 2.5. 3 Transformation Let us explain this category of spatial access methods by means of Space Filling Curves, [22] which are used for representing extended objects by a list of grid cells or a list of one dimensional intervals. In short, space filling curves try to store points, which are close in space, i.e. logical order, also close on disk, i.e. physical order. To put it in other words, these methods try ....

....of the Hilbert Curves, which can be generalised for higher dimensionalities. In this case, the order tends to infinity where the result is a fractal. To sum it up, this kind of space filling curve imposes a linear ordering on the grid points according to a fractal. For more details, we refer to [22]. We can now specify the main characteristics of a Hilbert R tree [41] behaves like an R tree . supports deferred splitting on insertion by means of the Hilbert value of the inserted data rectangle as the primary key What is more, for every node n of the tree, the . MBR and . Largest ....

C. Faloutsos, S. Roseman, Fractals for Secondary Key Retrieval, Proceedings of ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, 1989.

....domain, e. g, in parallel gravitational particle simulation [26] for graph partitioning [14] and fast range queries for geometrical data stored on disks [3, 4] Whenever there is a requirement for some kind of locality in mesh indexings, space lling curves, and, in particular Hilbert indexings [2, 3, 4, 6, 7, 9, 10, 12, 13, 23, 25] seem to come into play. Gotsman and Lindenbaum [10] study 1 r locality for the Euclidean metric that plays an important role in elds such as image processing and computer graphics. They primarily consider Hilbert s space lling curve and provide upper and lower bounds. We improve their upper ....

C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In 8th ACM Symposium on Principles of Database Systems, pages 247-252, 1989.

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Faloutsos C., Roseman S. "Fractals for Secondary Key Retrieval." Proceedings of the Eighth ACM SIGACT-SIGMID-SIGART Symposium on Principles of Database Systems (PODS). 1989

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C. FALOUTSOS AND S. ROSEMAN, Fractals for secondary key retrieval, in Proceedings of the Eighth ACM SIGACT-SIGMIDSIGART Symposium on Principles of Database Systems (PODS), 1989.

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Christos Faloutsos and Shari Roseman. Fractals for secondary key retrieval. In Proceedings of the Eighth ACM SIGACT-SIGMID-SIGART Symposium on Principles of Database Systems (PODS), 1989.

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C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In Proceedings of the Eighth ACM SIGACTSIGMID -SIGART Symposium on Principles of Database Systems (PODS), 1989.

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C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In the 8th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Philadelphia, PA, Mar. 1989.

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C. Faloutsos, S. Roseman. Fractals for secondary key retrieval, In Proc. of the ACM SIGACT/ SIGMOD Symposium on Principles of Database Systems, March 1989.

No context found.

C. Faloutsos and S. Roseman. Fractals for secondary key retrieval. In Proceedings of the Eighth ACM SIGACTSIGMID -SIGART Symposium on Principles of Database Systems (PODS), 1989.

No context found.

Faloutsos C., Roseman S. "Fractals for Secondary Key Retrieval." Proceedings of the Eighth ACM SIGACT-SIGMID-SIGART Symposium on Principles of Database Systems (PODS). 1989

No context found.

C. Faloutsos, S. Roseman. Fractals for secondary key retrieval, In Proc. of the ACM SIGACT/ SIGMOD Symposium on Principles of Database Systems, March 1989.

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C. Faloutsos and S. Roseman. Fractals for Secondary Key Retrieval. In Proc. PODS, pp. 247--252, 1989.

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Faloutsos C, Roseman S (1989) Fractals for Secondary Key Retrieval. Proceedings of ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS), pp 247-252

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C. Faloutsos, S. Roseman. Fractals for secondary key retrieval, In Proc. of the ACM SIGACT/ SIGMOD Symposium on Principles of Database Systems, March 1989.

No context found.

Christos Faloutsos and Shari Roseman. Fractals for secondary key retrieval. In Proceedings of the Eighth ACM SIGACT-SIGMID-SIGART Symposium on Principles of Database Systems (PODS), 1989.

No context found.

C. Faloutsos and S. Roseman. Fractals for Secondary Key Retrieval. In Proc. 8th ACM PODS, pages 247-- 252, Philadelphia, PA, 1989. 4

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