H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[25] Hilbert curve method [12, 19] lattice allocation method [10] and cyclic allocation scheme [32] These methods are briefly discussed in Section 2.2. A remarkable declustering method is using error correcting codes in order to partition binary strings into groups of unsimilar strings [8, 11, 12, 13]. The method is based on the idea of providing the strings in a group have large Hamming distances by grouping the strings in such a way that each group forms an error correcting code. The method was applied to problems such as declustering cartesian product files [11] grid files [7, 12] and ....

....unsimilar strings [8, 11, 12, 13] The method is based on the idea of providing the strings in a group have large Hamming distances by grouping the strings in such a way that each group forms an error correcting code. The method was applied to problems such as declustering cartesian product files [11], grid files [7, 12] and signature files [8] Local Load Balance (LLB) methods [21, 35] define a local window around the data item to be allocated, and map this data item to the disk with minimum load over the local window. This method was applied to parallelizing R trees [21] and parallelizing ....

H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple disk systems. ACM Trans. Database Systems, 7(1):82--101, 1982.

....I O devices such that neighboring partitions are allocated to different disks. Performance improvements for queries occur when the buckets involved in query processing are stored on different disks, and hence can be retrieved in parallel. Numerous methods have been proposed: Disk Modulo (DM) [6], Hilbert (HCAM) 8] Near Optimal Declustering (NoD) 2] General Multidimensional Data Allocation (GMDA) 15] and the Cyclic Allocation Schemes [17] All of these approaches were based on non overlapping rectangular partitions. Another successful application of regular partitioning is the vector ....

....assignments of each partitions on that disk, assuming that there are five disks in the system. The disk allocation is needed for declustering and the page allocation is needed for clustering purposes. The disk assignment in Figure 8(a) is developed by applying the Disk Modulo (DM) declustering [6] for hexagonal partitioning. We assign the pages in row major order for each disk. In general, given a partition, PartitionId = i; j) where i is the row number and j is the column number, the physical location of the partition, i.e. the corresponding disk and the page within that disk, can be ....

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H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

....[17] to determine appropriate H values can also be used here. In addition to cyclic allocation, there have been a number of other disk allocation techniques proposed for regular grid partitioning, especially in the context of relational data and partial match and range queries. Disk Modulo (DM) [9], Fieldwise Exclusive (FX) 16] Hilbert (HCAM) 12] Near Optimal Declustering (NoD) 5 0 20 40 60 80 100 120 0 0.5 1 1.5 2 2.5 3 3.5 4 Query Radius OPTIMAL VERSUS OTHER PARTITIONING TECHNIQUES Optimal Approximation Fully wedged Concentric Figure 6: The performance of different ....

H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82-- 101, March 1982.

....response time of queries is to decluster data across a set of disks in order to exploit parallelism at the I O level [PGK88] Many algorithms for multi attribute declustering, aiming to efficiently support multi dimensional range queries, today exist. Methods based on declustering functions DM [DS82], CMD [LSR92] FX [KP88] ECC [FM91] HCAM [FB93] and others operate by first partitioning the data space into an orthogonal grid, and then mapping each cell of the grid to a specific disk. Since the mapping from space regions to disks is static, these methods cannot efficiently manage cases ....

....coordinates, I 1 ; I 2 2 [0; S Gamma 1] Each declustering method, met , maps cell identifiers (coordinates) into disk identifiers by using the diskOf met ( function, that is: diskOf met : 0; S Gamma 1] Theta [0; S Gamma 1] 0; M Gamma 1] Example 1. The disk modulo (DM) method [DS82] is defined as: 3 diskOfDM (I 1 ; I 2 ) I 1 I 2 ) mod M whereas the error correcting codes (ECC) method [FM91] which requires M = 2 m (m 1) and S = 2 s , declusters grid cells by means of the parity check matrix of a binary code. Cell coordinates are represented using s bits each, ....

H.C. Du and J.S. Sobolewski. Disk allocation for Cartesian product files on multiple disk systems. ACM Transactions on Database Systems, 7(1):82--101, March 1982.

....I O devices such that neighboring partitions are allocated to different disks. Performance improvements for queries occur when the buckets involved in query processing are stored on different disks, and hence can be retrieved in parallel. Numerous methods have been proposed: Disk Modulo (DM) [6], Hilbert (HCAM) 8] Near Optimal Declustering (NoD) 2] General Multidimensional Data Allocation (GMDA) 15] and the Cyclic Allocation Schemes [17] All of these approaches were based on non overlapping rectangular partitions. Another successful application of regular partitioning is the vector ....

....partitions with 6 rows and 6 columns. The labels in the figure specifies the disks as well as the page assignments of each partitions on that disk, assuming that there are five disks in the system. The disk assignment in Figure 8(a) is developed by applying the Disk Modulo (DM) declustering [6] for hexagonal partitioning. We assign the pages in the row major order for each disk. In general, given a partition, PartitionId = i; j) where i is the row number and j is the column number, the physical location of the partition, i.e. the corresponding disk and the page within that disk, can ....

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H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982. 13

....in relational databases. good way of declustering good Declustering or disk allocation has been extensively This work was partially supported by NSF grant CCR97 12108. studied in the past especially in the context of relational data and partial match and range queries. Disk Modulo (DM) [6], Fieldwise Exclusive (FX) 10] Hilbert (HCAM) 7] Near Optimal Declustering (NoD) 2] General Multidimensional Data Allocation (GMDA) 9] Cyclic Allocation Schemes [11, 12] are the well known techniques. In these methods, the data space is first split into equi sized partitions along each ....

H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

....are similar to grid files; the primary difference between the two structures is that every subspace in a Cartesian product file is stored in a separate disk page whereas subspaces in grid files can, and often are, merged to conserve space. We extend the three best known schemes, disk modulo (DM)[2], fieldwise xor(FX) 12] and Hilbert curve(HCAM) 3] for grid files. By simulation experiments, we show that the scalability of DM and FX for multidimensional range queries is limited. That is, as the number of disks is increased beyond a threshold, the response time no longer decreases. This ....

....the scalability of these schemes for multidimensional range queries is limited. The disk modulo (DM) scheme assigns each subspace (or bucket #i 1 ;i 2 ; i d # in a Cartesian product file) to the disk unit number #i 1 i 2 : i d#mod M where M is the number of disks. It has been shown in [2] that the disk modulo is strictly optimal for many cases of partial match queries including all partial match queries with only one unspecified attribute. By partial match queries we mean queries of the form #A 1 = a 1 ;A2 = a2 ; A d = a d#where for each i # i # d, a i is either a key belonging ....

H. C. Du and J. S. Sobolewski. Disk allocation for Cartesian product files on multiple-disk systems. ACM Trans. Database Syst., 7(1):82--101, Mar. 1982.

....subspace can be assigned to more than one disk. Another classification of declustering methods can be on whether the partitioning of the data space is done in terms of regular grids, e.g. grid file [15] type partitioning, or irregular shapes. While 2 most proposals have been in the first category [9] [17] 10] 18] 11] there have been some proposals in the second category [13] While the question of whether regular or irregular partitions are better is by no means settled, the two approaches would require different types of directory structures and their performances cannot be directly ....

....partitioned into subspaces using a grid based partitioning. ffl There is no data replication. ffl A data subspace is assigned to exactly one disk. The declustering problem as posed above is also referred to as the Cartesian Product file allocation problem. Since Du s disk modulo (DM) proposal [9] a decade ago, a number of techniques have have been proposed for this problem. Du generalized his original proposal to the generalized disk modulo (GDM) method. Both of these approaches are based on numbering the partitions on each dimension of the data space by integers. A data subspace is ....

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H.C. Du and J.S. Sobolewski. Disk allocation for cartesian product files on multiple disk systems. ACM Transcations on Database Systems, pages 82--101, March 1982.

....subspace can be assigned to more than one disk. Another classification of declustering methods can be on whether the partitioning of the data space is done in terms of regular grids, e.g. grid file [19] type partitioning, or irregular shapes. While most proposals have been in the first category [4] [17] 6] 14] 5] there have been some proposals in the second category [11] Though the question of whether regular or irregular partitions are better is by no means settled, our focus here is to find a good declustering method for regular grid based partitioning. Thus, the characteristics of ....

....ffl The data space is partitioned into subspaces using a grid based partitioning. ffl A data subspace is assigned to exactly one disk. The declustering problem as posed above is also referred to as the Cartesian Product file declustering problem. Since Du s disk modulo (DM) proposal [4] a decade ago, a number of techniques have have been proposed for this problem. Du generalized his original proposal to the generalized disk modulo (GDM) method. Both of these approaches are based on numbering the partitions on each dimension of the data space by integers. A data subspace is ....

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H.C. Du and J.S. Sobolewski. Disk allocation for cartesian product files on multiple disk systems. ACM Transactions on Database Systems, pages 82--101, March 1982.

.... methods have been developed to decluster a Cartesian product file [32] which has been known as a multi attribute file structure effective for partial match and best match queries [40] There are a few well known multidimensional declustering methods for Cartesian product files: Disk Modulo (DM) [14], Fieldwise Xor (FX) 30] Error Correcting Codes (ECC) 17] Hilbert Curve Allocation Method (HCAM) 16] and Vector based declustering method [7] Although ample analytic studies have been done for partial match queries [1, 14, 30, 45] relatively little attention has been focused on range ....

.... declustering methods for Cartesian product files: Disk Modulo (DM) 14] Fieldwise Xor (FX) 30] Error Correcting Codes (ECC) 17] Hilbert Curve Allocation Method (HCAM) 16] and Vector based declustering method [7] Although ample analytic studies have been done for partial match queries [1, 14, 30, 45], relatively little attention has been focused on range queries [31] To the best of authors knowledge, no analytic results have been provided so far for the scalability of multidimensional declustering methods with varying number of disks. The scalability of declustering methods becomes ....

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H. C. Du and J. S. Sobolewski. Disk allocation for Cartesian product files on multiple-disk systems. ACM Transactions on Database Systems, 7(1):82--101, March 1982.

....will use the term disk to refer to such data banks, parallel disks, or nodes. The goal of the allocation is to achieve optimal parallel access for each range query. The design of these allocation schemes has been an active research area, resulting in the development of several allocation schemes [5, 7, 6, 1, 9]. These schemes are developed under the following framework. Due to the relatively high cost of disk accesses, the CPU processing time is ignored. Furthermore, since the disk accesses are random, the cost of a single disk access is assumed to be constant. Note that for the case of main memory ....

....; xd Gamma1 ) Each coordinate, x j , is in the range [0; N j Gamma 1] and represents the order of the block in dimension j, where dimension j is divided into N j blocks. The number of disks is k, and each disk is identified by a number ranging from 0 to k Gamma 1. The Disk Modulo (DM) scheme [5], developed by Du and Sobolewski and later extended for range queries and dynamic files in [8] allocates block (x0 ; Delta Delta Delta ; xd Gamma1 ) to disk (x0 x1 Delta Delta Delta xd Gamma1 ) mod k. The Fieldwise eXclusive (FX) method proposed by Kim and Pramanik [7] allocates a ....

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H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

....parallel. On the other hand, if they are allocated to the same device, response time is maximized, since the information associated with the different tiles must be retrieved sequentially instead of concurrently. Various proposals have been made for the allocation of data on multiple I O devices [DS82, KP88, FB93, BBB 97, PAE 97] The effectiveness of disk allocation in reducing the response time for range queries has also been demonstrated based upon simulation [GD90, GDQ92] Many of these were made in the context of relational databases, where data is defined over several attributes. ....

....for methods that give good performance for the cases for which no strictly optimal solution exists. Several allocation methods have been proposed in the literature. We begin by discussing these existing methods and evaluating their performance. These methods are: ffl The Disk Modulo method (DM) DS82] ffl The FX method [KP88] ffl The HCAM method [FB93] The Disk Modulo approach proposed by Du and Sobolewski was designed to allocate Cartesian product files to multiple disks to improve the performance of partial match queries. The approach was later extended by Li, Srivastava and Rotem for ....

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H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

....the response time of the query is dominated by the access time of the disk that holds the most numbers of tiles in the query. Various declustering schemes have been proposed to reduce the response time for multidimensional queries, including those proposed specifically for uniform data grids [11, 17, 12, 10, 20, 8] and those that are more suitable for non uniform data grids [13, 19, 22, 7] In this paper, we concentrate on declustering for uniform data grids. Recently, it was shown [20] that the Cyclic Declustering (CD) scheme a simple generalization of the Disk Modulo scheme [11] outperforms the ....

....grids [11, 17, 12, 10, 20, 8] and those that are more suitable for non uniform data grids [13, 19, 22, 7] In this paper, we concentrate on declustering for uniform data grids. Recently, it was shown [20] that the Cyclic Declustering (CD) scheme a simple generalization of the Disk Modulo scheme [11] outperforms the previously known best data declustering schemes such as the Hilbert Curve Allocation Method (HCAM) 12] In this paper, we propose a new declustering scheme based on the Golden Ratio Sequences (GRS) The GRS are highly regular sequences in which elements of certain sets are ....

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H.C. Du and J.S. Sobolewski. Disk allocation for cartesian product files on multiple disk systems. ACM Trans. Database Systems, pages 82--101, 1982.

....declustering and no closed form solution is presented. Chen and Chang in [CC92] study the disk modulo allocation method for range queries and give sufficient (but not necessary) conditions for strict optimality. This method was originally developed by Du and Sobolewski for partial match queries [DS82] For two dimensions, and using the language of our paper, the allocation method assigns the number x y mod M to the tile represented by (x; y) It is shown in [CC92] that the method is strictly optimal if M = 2 or 3. This result, in two dimensions, follows from Lemma 1 which states that the ....

H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Trans. Database Syst., 7(1):82--101, 1982.

....aiming to minimize the number of data blocks fetched from a single disk and thereby minimizing query processing time. Numerous declustering methods have been reported in the literature. For multidimensional datasets, such declustering methods can be classified into two approaches: grid based [3, 6, 9] and graph theoretic [10, 20, 21] Grid based methods have been developed to decluster Cartesian product files, while graph theoretic methods are aimed at declustering more general spatial access structures such as grid files [25] and R trees [14] A survey of declustering methods can be found ....

....3: Bounding boxes covering 12 land masses time required for one disk access to retrieve a block. Ignoring the effects of disk caching, the maximum number of data blocks fetched from the same disk (i.e. max M i=1 fN i (q)g) is considered a plausible measure of the actual block transfer time [6, 21]. Definition 2 A cluster of blocks is a group of data blocks that are contiguous on disk. 3 Then, given a query q, the model seek time is defined to be the number of clusters in the answer set of q. The metric given in Definition 2 was originally proposed in [15] and used to analyze the ....

H. C. Du and J. S. Sobolewski. Disk allocation for Cartesian product files on multiple-disk systems. ACM Transactions on Database Systems, 7(1):82--101, March 1982.

....accessed attribute of the relation. In contrast, our strategy is based on the most frequently evoked method of the class. Furthermore, the single hashing attribute is the object identifier, since in OODBs objects are usually accessed through that. Thus, multi attribute declustering strategies [11, 15, 20, 21] do not apply to our case, except if they are adapted for multiple methods. In the following sub section, the analytical performance of PRISMA DB query execution is summarized as background knowledge, because it will be used as a measure of comparison with our analysis. 2.1. Background The ....

H. Du, J. Sobolewski, Disk allocation for cartesian product files on multiple disk systems, ACM Trans. Database Systems, 7(1) (1982) 82-101.

....of a relation into fragments based on the values of one or several attributes. Among the schemes employed for single attribute partitioning are hashing and range partitioning [18,27] while techniques based on Cartesian product files have been advocated for multiple attribute declustering (e.g. [20, 21, 29, 44]) Striping has an advantage over application level methods in that it can be applied as a generic low level method for a wide spectrum of data types (all of which are ultimately mapped into block structured files) In this paper, we therefore restrict our attention to data partitioning via file ....

Du HC, Sobolewski JS (1982) Disk Allocation for Cartesian Product Files on Multiple Disk Systems. ACM Trans Database Syst 7(1): 82-- 101

....across processors, assuming that the queries or the joins involve only one attribute. A large number of methods have been proposed in the past, aiming to achieve good declustering for partial match queries, that refer to several attributes. Almost all these methods focus on Cartesian Product Files [8]. Among the few exceptions is the work in [22] where records are dynamically relocated, to avoid hot spots . All the rest of the declustering methods assume that the allocation of buckets to disks does not change over time. A survey of such declustering methods can be found in [9] There, the ....

....Assign buckets to units (i.e. determine the diskOf( function) so that the average response time for range queries is minimized. Next we describe briefly the major representatives of some older declustering methods. 2. 1 Disk Modulo Allocation Method (DM) In the Disk Modulo allocation method [8], each bucket [i 1 ; i 2 ; i k ] is assigned to disk unit diskOf(i 1 ; i 2 ; i k ) i 1 i 2 : i k ) mod M (1) For example, consider a relation R with two attributes, R(X; Y ) Suppose that each domain is divided into 8 ranges (d 1 = d 2 = 8) Thus, relation R consists ....

H.C. Du and J.S. Sobolewski. Disk allocation for cartesian product files on multiple disk systems. ACM Trans. Database Systems (TODS), 7(1):82--101, March 1982.

....p0 Delta Delta Delta cD Gamma1 Theta pD Gamma1 ) mod M , where (p0 ; pD Gamma1 ) are called the GDM parameters. In [16] we proposed a method to pick GDM parameters for datasets of any dimension, called GDM Cartesian. We demonstrated that GDM Cartesian significantly outperforms DM [10], FX [14] Hilbert curve [11] Vector based [4] HalfM and Fibonacci [21] on average, for the set of all possible range queries. Thus, for the experiments described in this paper, we used GDM Cartesian to decluster chunks. Due to space constraints, we refer the reader to [16] for a full ....

H. Du and J. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions on Database Systems, 7(1):82--101, March 1982.

....multiple disks has been well studied in the context of relational databases, where the goal has been to improve the performance of range and partial match queries. Prominent examples of such declustering schemes are HCAM [FB93] Fieldwise Exclusive or FX [KP88] and CMD [LSR92] or Disk Modulo [DS82] and error correcting based techniques [FM89, AE93] In [BBB 97] a new declustering technique is developed that optimizes data allocation on multiple disks for nearest neighbor queries. The authors argue that the existing declustering techniques do not generate adequate declustering for ....

....x j is in the range [0; N j Gamma 1] since dimension j is divided into N j parts. Also, M represents the number of disks over which the buckets are to be declustered, and d is the number of dimensions. The meaning of each symbol is summarized in Table 1. The Disk Modulo or DM approach [DS82] allocates bucket (x 0 ; x 1 ; Delta Delta Delta ; x d Gamma1 ) to disk ( d Gamma1 X j=0 x j ) mod M: The Fieldwise eXclusive or FX approach [KP88] allocates the same bucket to disk (b 0 Phi b 1 Phi Delta Delta Delta Phi b d Gamma1 ) mod M where b j is the binary representation of x ....

H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multipledisk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

....keys would be located on the same disk. Using analogous arguments, choosing disk number 2 or 3 leads to an optimization for key range queries at the expense of poor performance for time range queries. The problem of multidimensional declustering has been intensively studied for static data [DS82, FM91, FB93, GD94, HS94,KP88, ZSC94], but is more or less unexplored for the dynamic case considered here. Thus, generalizing the local balancing method of [SL91] to the TSB tree is not at all straightforward. We simplify this problem by breaking it up into two independent tasks. Namely, we handle current and historical nodes ....

Du, H.C., Sobolewski, J.S., Disk Allocation for Cartesian Product Files on Multiple Disk Systems, ACM Transactions on Database Systems Vol. 7 No.1, 1982, pp. 82-101

....can be retrieved from multiple devices in parallel. On the other hand, if they are allocated to the same device, response time is maximized, since the tiles must be retrieved sequentially instead of concurrently. Various proposals have been made for the allocation of data on multiple I O devices [DS82, KP88, FB93] Some of these studies were conducted in the context of relational databases, where data is defined over several attributes. We address the important but restricted case of two attributes (the x and y coordinates of twodimensional data) Recently in [AE97] it was shown that strictly ....

....that except for these restricted cases, no strictly optimal allocation exists, in this paper we look for methods that give good performance for the cases for which no strictly optimal solution exists. Several allocation methods have been proposed in the literature. The Disk Modulo (DM) DS82] approach proposed by Du and Sobolewski and later extended for range queries and dynamic files in [LSR92] allocates tile (i; j) to device (i j) mod M . The FX method proposed by Kim and Pramanik [KP88] requires that N 1 ; N 2 and M are all powers of 2. The tile (i; j) is then allocated to the ....

[Article contains additional citation context not shown here]

H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

....a relation into fragments based on the values of one or several attributes. Among the schemes employed for single attribute partitioning are hashing and range partitioning [18, 27] while techniques based on Cartesian product files have been advocated for multiple attribute declustering (e.g. [20, 21, 29, 44]) Striping has an advantage over application level methods in that it can be applied as a generic low level method for a wide spectrum of data types (all of which are ultimately mapped into block structured files) In this paper we therefore restrict our attention to data partitioning via file ....

Du, H.C., Sobolewski, J.S., Disk Allocation for Cartesian Product Files on Multiple Disk Systems, ACM Transactions on Database Systems Vol. 7 No.1, 1982, pp. 82-101

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H. C. Du and J. S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

No context found.

H.C. Du and J.S. Sobolewski. Disk allocation for cartesian product files on multiple-disk systems. ACM Transactions of Database Systems, 7(1):82--101, March 1982.

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