## Multidimensional declustering schemes using golden ratio and kronecker sequences (2003)

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Venue: | In IEEE Trans. on Knowledge and Data Engineering |

Citations: | 2 - 0 self |

### BibTeX

@ARTICLE{Chen03multidimensionaldeclustering,

author = {Chung-min Chen and Randeep Bhatia and Rakesh K. Sinha},

title = {Multidimensional declustering schemes using golden ratio and kronecker sequences},

journal = {In IEEE Trans. on Knowledge and Data Engineering},

year = {2003},

volume = {15},

pages = {2003}

}

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### Abstract

### Citations

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The Art of computer programming
- Knuth
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Citation Context ... are highly regular sequences in which elements of certain sets are almost uniformly distributed. GRS sequences were developed in [21] and are based on an open addressing hashing method introduced in =-=[24]-=-. GRS sequences have also found applications in packet routing [20] and other optimization problems [4]. For declustering 2-dimensional data our scheme has the property that the data points getting as... |

132 |
Über die Gleichverteilung von Zahlen mod. Eins
- Weyl
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Citation Context ...ection 2.1). One good choice of the Kronecker parameters k is the class of quadratic irrationalities, which are numbers of the form u+ p v (or its multiples), with u; v rational and p v irrationals [=-=-=-36]. However, no explicit values seem to be known for ( 1 ; : : : ; d ) that will produce good d-dimensional Kronecker sequences. Nonetheless, it is natural to choose the values such that 1 and 1 ; ... |

113 | A case for intelligent disks (IDISKs
- Keetong, Patterson, et al.
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(Show Context)
Citation Context ...or high-performance systems that use hundreds or even thousands 1 The implementation is optimized with a dynamic programming technique that evaluates all queries with an M d grid. 6 of parallel disks =-=[22, 1, 30]-=-. Description and Comparison to schemes with (limited) analytical guarantees Subsequent to thesrst publication [6] of the GRS scheme described in this paper, a number of schemes with analytical guaran... |

85 | Minimizing service and operation costs of periodic scheduling - Bar-Noy, Bhatia, et al. - 2002 |

82 | Declustering Using Fractals
- Faloutsos, Bhagwat
- 1993
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Citation Context ... to design declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specically devised for uniform data [=-=13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35]-=-, and those that work for both uniform and non-uniform data [28, 15, 27, 31, 8]. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In co... |

78 | Titan: a highperformance remote-sensing database
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- 1997
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Citation Context ...been proposed for range queries, including those that are specically devised for uniform data [13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35], and those that work for both uniform and non-uniform data [=-=28, 15, 27, 31, 8]-=-. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In contrast, we propose a scheme with (limited) analytical guarantees on its perform... |

57 | Disk allocation for cartesian product files on multiple disk systems
- Du, Sobolewski
- 1982
(Show Context)
Citation Context ...to design declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specifically devised for uniform data =-=[13]-=-, [19], [14], [33], [29], [30], [21], [16], [6], [7], [2], [31], and those that work for both uniform and nonuniform data [15], [23], [27], [5]. In most of the prior work, performance is evaluated thr... |

52 |
Optimal file distribution for partial match retrieval
- Kim, Pramanik
- 1988
(Show Context)
Citation Context ...ign declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specifically devised for uniform data [13], =-=[19]-=-, [14], [33], [29], [30], [21], [16], [6], [7], [2], [31], and those that work for both uniform and nonuniform data [15], [23], [27], [5]. In most of the prior work, performance is evaluated through s... |

44 |
Parallel I/O for High Performance Computing
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Citation Context ...or high-performance systems that use hundreds or even thousands 1 The implementation is optimized with a dynamic programming technique that evaluates all queries with an M d grid. 6 of parallel disks =-=[22, 1, 30]-=-. Description and Comparison to schemes with (limited) analytical guarantees Subsequent to thesrst publication [6] of the GRS scheme described in this paper, a number of schemes with analytical guaran... |

43 | Abbadi, “Cyclic allocation of two-dimensional data
- Prabhakar, Abdel-Ghaffar, et al.
- 1998
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Citation Context ...t would minimize the query response time. An ideal declustering scheme would achieve, for each query Q, the optimal response time ORT (Q) = djQj=Me, where jQj is the number of tiles in Q. It is known =-=[37, 2]-=- that such a scheme, historically referred to as the Strictly Optimal (SO) scheme, does not exist for two-dimensional data, except for a few stringent cases. It is also known [35] that any d-dimension... |

43 | Geometric Discrepancy: An Illustrated Guide - Matou˘sek - 1999 |

38 | CMD: A Multidimensional Declustering Method for Parallel Database Systems
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- 1992
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Citation Context ...Wesrst describe the schemes that do not provide any analytical guarantees on their general performance, though optimality for some special shapes of range queries are achievable. The Disk Modulo (DM) =-=[13, 26] and -=-the Field Exclusive-Or (FX) [23] schemes are two of the earliest work on declustering. Both schemes were intended for \partial match" queries, a special case of range queries where the range on e... |

35 | Partitioning Similarity Graphs: A Framework for Declustering Problems
- Shekhar, DLiu
- 1996
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Citation Context ...been proposed for range queries, including those that are specically devised for uniform data [13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35], and those that work for both uniform and non-uniform data [=-=28, 15, 27, 31, 8]-=-. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In contrast, we propose a scheme with (limited) analytical guarantees on its perform... |

32 | Almost) Optimal Parallel Block Access for Range Queries
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- 2000
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Citation Context ... to design declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specically devised for uniform data [=-=13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35]-=-, and those that work for both uniform and non-uniform data [28, 15, 27, 31, 8]. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In co... |

32 |
The idea of de-clustering and its applications
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Citation Context ...been proposed for range queries, including those that are specically devised for uniform data [13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35], and those that work for both uniform and non-uniform data [=-=28, 15, 27, 31, 8]-=-. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In contrast, we propose a scheme with (limited) analytical guarantees on its perform... |

30 |
Declustering Objects for Visualization
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Citation Context ...that is to be stored, without fragmentation, on one of the disks. Raster-spatial data are typically arranged in this format and can be found in applications such as remote-sensing and image databases =-=[18, 12, 19, 10]-=-. An important class of queries in multidimensional data is range query. A range query requests a hyper-rectangular subset of the multidimensional data space. As a result, all data tiles that overlap ... |

26 | Declustering Using Golden Ratio Sequences
- Bhatia, Sinha, et al.
- 2000
(Show Context)
Citation Context ... to design declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specically devised for uniform data [=-=13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35]-=-, and those that work for both uniform and non-uniform data [28, 15, 27, 31, 8]. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In co... |

24 |
A Golden Ratio Control Policy for a Multiple-Access Channel
- Itai, Rosberg
- 1987
(Show Context)
Citation Context ...quent to [6], four more schemes [7, 3, 35, 28] have been proposed giving some form of analytical guarantees. We propose a two-dimensional declustering scheme, GRS, based on the Golden Ratio Sequences =-=[21]-=- and a multi-dimensional declustering scheme based on the Kronecker Sequences[5]. (The multi-dimensional scheme is a substantial improvement over the scheme 2 proposed in the conference version of thi... |

24 | Study of Scalable Declustering Algorithms for Parallel Grid Files
- Moon, Acharya, et al.
- 1996
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Citation Context |

23 | Abbadi, “Concentric hyperspaces and disk allocation for fast parallel range searching
- Ferhatosmanoglu, Agrawal, et al.
- 1999
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Citation Context |

23 |
The Art of Computer Programming, vol 3
- Knuth
- 1973
(Show Context)
Citation Context ... are highly regular sequences in which elements of certain sets are almost uniformly distributed. GRS sequences were developed in [21] and are based on an open addressing hashing method introduced in =-=[24]-=-. GRS sequences have also found applications in packet routing [20] and other optimization problems [4]. For declustering 2-dimensional data our scheme has the property that the data points getting as... |

22 |
Hierarchical Declustering Schemes for Range Queries
- Bhatia, Sinha, et al.
- 2000
(Show Context)
Citation Context ...to design declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specifically devised for uniform data =-=[13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35]-=-, and those that work for both uniform and non-uniform data [28, 15, 27, 31, 8]. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In co... |

21 | From discrepancy to declustering: Near optimal multidimensional declustering strategies for range queries
- Chen, Cheng
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Citation Context ...e for 8 queries of all possible shapes. Our simulation (presented in Sections 6 and 7) shows that GRS outperforms GeMDA both in terms of worst case as well as average case performance. Very recently, =-=[9-=-] described a scheme with guaranteed worst case performance for any dimensions. The scheme, however, is dened only when M is a prime number and takes exponential time to construct. Its performance in ... |

20 |
Packet Delay under the Golden Ratio Weighted TDM Policy in a Multiple-Access Channel
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Citation Context ... almost uniformly distributed. GRS sequences were developed in [21] and are based on an open addressing hashing method introduced in [24]. GRS sequences have also found applications in packet routing =-=[20]-=- and other optimization problems [4]. For declustering 2-dimensional data our scheme has the property that the data points getting assigned to the same disk are selected based on the GRS sequence, thu... |

18 |
Disk Allocation Methods for Parallelizing Grid Files
- Zhou, Shekhar, et al.
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Citation Context ...ring schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are specifically devised for uniform data [13], [19], [14], =-=[33]-=-, [29], [30], [21], [16], [6], [7], [2], [31], and those that work for both uniform and nonuniform data [15], [23], [27], [5]. In most of the prior work, performance is evaluated through simulation wi... |

9 | Efficient retrieval of multidimensional datasets through parallel I/O
- Prabhakar, Abdel-Ghaffar, et al.
- 1998
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Citation Context ...d 1, k = 0; 1; : : : ; M 1. In other words, the last d t dimensions are declustered as a Disk Modulo scheme [13]. This is undesirable as we know Disk Modulo gives poor performance for range queries [=-=14,-=- 34]. The problem can be easilysxed. Observe that the golden ratio = 2 1+ p 5 can be equivalently expressed as = 1+ p 5 2 . We now choose k = 1+ p p k 2 to generate permutation k . For large k, th... |

9 | Clustering Declustered Data for Efficient Retrieval
- Ferhatosmanoglu, Agrawal, et al.
(Show Context)
Citation Context ...m is the intra-disk placement of blocks going to the same disk. This is an independent problem and a good scheme for intra-disk placement problem can be combined with a good declustering scheme (e.g. =-=[16]-=-). In this paper, we restrict ourselves to the declustering problem. The rest of the paper is organized as follows. In the next section we formally define the declustering problem and the GRS decluste... |

8 |
Dealing with the data deluge
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- 1993
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Citation Context ...ion of very large databases. A good example is NASA's Earth Science Enterprise projects, which are expected to receive terabytes of remote-sensed data daily from the satellites when in full operation =-=[18-=-]. A preliminary version of this paper appeared in the 16th International Conference on Data Engineering, ICDE 2000. The last two authors did this work at Bell Laboratories. y Corresponding author. T... |

7 |
Probabilistic diophantine approximation, I Kronecker sequences
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Citation Context ...m of analytical guarantees. We propose a two-dimensional declustering scheme, GRS, based on the Golden Ratio Sequences [21] and a multi-dimensional declustering scheme based on the Kronecker Sequences=-=[5]-=-. (The multi-dimensional scheme is a substantial improvement over the scheme 2 proposed in the conference version of this paper [6].) We present comprehensive simulation results, showing that our sche... |

6 |
Analysis and comparison of declustering schemes for interactive navigation queries
- Chen, Sinha
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Citation Context ...red, without fragmentation, on one of the disks. Raster-spatial data are typically arranged in this format and can be found in applications such as remote-sensing and image databases [17], [12], [8], =-=[11]-=-. An important class of queries in . C.-M. Chen is with Telcordia Technologies, 445 South St., Morristown, New Jersey. E-mail: chungmin@research.telcordia.com. . R. Bhatia is with Bell Labs, 600 Mount... |

5 |
On GDM allocation method for partial range queries
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Citation Context ... is more expensive to obtain due to its O(M 4 ) search overhead. 6.2. Average Case Performance Fixing M and a grid size, there are various ways to dene \average performance" of a declustering sch=-=eme [11, 33, 34, 25-=-]. We will adopt the convention of measuring the ratio 20 1 1.1 1.2 1.3 1.4 1.5 1.6 0 20 40 60 80 100 120 number of disks GeMDA GFIB EXH GRS Figure 3: Perf. (average-by-all) for 32 32 grid 1 1.05 1.1... |

5 |
New gdm-based declustering methods for parallel range queries
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4 |
Raster-spatial data declustering revisited: an interactive navigation perspective
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Citation Context ...that is to be stored, without fragmentation, on one of the disks. Raster-spatial data are typically arranged in this format and can be found in applications such as remote-sensing and image databases =-=[18, 12, 19, 10]-=-. An important class of queries in multidimensional data is range query. A range query requests a hyper-rectangular subset of the multidimensional data space. As a result, all data tiles that overlap ... |

4 |
Disk allocation for cartesian product on multiple-disk systems
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Optimal distribution for partial match retrieval
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3 | Minimizing Service and - Bar-Noy, Bhatia, et al. - 1998 |

3 |
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Citation Context ...e queries, including those that are specifically devised for uniform data [13], [19], [14], [33], [29], [30], [21], [16], [6], [7], [2], [31], and those that work for both uniform and nonuniform data =-=[15]-=-, [23], [27], [5]. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. One exception is [24], which gives optimal response time for hyperc... |

2 |
Abbadi. Clustering declustered data for ecient retrieval
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Citation Context ...m is the intra-disk placement of blocks going to the same disk. This is an independent problem and a good scheme for intra-disk placement problem can be combined with a good declustering scheme (e.g. =-=[16-=-]). In this paper, we restrict ourselves to the declustering problem. The rest of the paper is organized as follows. In the next section we formally dene the declustering problem and the GRS decluster... |

2 |
Storage of spatial data in a semantic database
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Citation Context ...that is to be stored, without fragmentation, on one of the disks. Raster-spatial data are typically arranged in this format and can be found in applications such as remote-sensing and image databases =-=[18, 12, 19, 10]-=-. An important class of queries in multidimensional data is range query. A range query requests a hyper-rectangular subset of the multidimensional data space. As a result, all data tiles that overlap ... |

2 |
GeMDA: A multidimensional data partitioning technique for multiprocessor database systems
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2 |
Asymptotically optimal declustering schemes for 2-dim range queries. Theoret
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1 |
Disk allocation methods for parallelizing grid
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1 |
Probabilistic Diophantine Approximation
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Citation Context ...m of analytical guarantees. We propose a two-dimensional declustering scheme, GRS, based on the Golden Ratio Sequences [18] and a multidimensional declustering scheme based on the Kronecker Sequences =-=[4]-=-. (The multidimensional scheme is fundamentally different from and is a substantial improvement over the one proposed in [6].) We present comprehensive simulation results, showing that our schemes per... |

1 |
Declustering Using Golden Ratio and Kronecker Sequences,” technical report, Applied Research,Telcordia Technologies
- Chen, Bhatia, et al.
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Citation Context ...the size of Q in the above definition). Fortunately, a permutation scheme is defined by a permutation of length M so the scheme has enough symmetry to admit an OðM4Þ algorithm for computing EðMÞ [6], =-=[9]-=-. We were able to obtain the additive errors for GRS and GFIB for up to 550 disks. Because of the longer computation time requirements of EXH and GeMDA, we only have results for up to 223 disks for EX... |

1 |
Personal Communication
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Citation Context ...me in Three Dimensions There are two different multidimensional versions of the coloring scheme, NEW1 and NEW2, proposed in [2]. NEW1 also has a variant that was not explicitly described in the paper =-=[28]-=-. We will call this third scheme NEW1-r. The NEW1 strategy requires M 2ðd 1Þt , for some integer t. In three dimensions, M 22t pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi . NEW1 colors a M ... |

1 |
die gleichverteilung von zahlem mod eins
- Uber
- 1916
(Show Context)
Citation Context ...ction 2.1). One good choice of the Kronecker parameters ffk is the class of quadratic irrationalities, which are numbers of the form u + p v (or its multiples), with u; v rational and p v irrationals =-=[36]-=-. However, no explicit values seem to be known for (ff1; : : : ; ffd) that will produce good d-dimensional Kronecker sequences. Nonetheless, it is natural to choose the values such that 1 and ff1; : :... |