Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

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86 5. Pre-Aggregation Support Beyond Basic Aggregate Operations • Dataset R2. Consists of a 3D raster object with spatial domain [0 : 11299, 0 : 10459, 0 : 3650]. The dataset contains 3214 tiles, each with a spatial domain of [0 : 512, 0 : 512, 0 : 512]. The total number of cells composing the raster object is 43 trillions. • Dataset R3. Consists of a 4D raster object with spatial domain [0 : 10150, 0 : 7259, 0 : 2430, 0 : 75640]. The dataset contains 197,070 tiles, each with a spatial domain of [0 : 512, 0 : 512, 0 : 512, 0 : 512]. The total number of cells composing the raster object is 1.35e+16. In the rest of this section, we present the results of our experiments according to the dimensionality of the data. 5.5.1 2D Datasets In this experiment the workload consisted of 12800 scaling operations defined for dataset R1. Uniform Distribution The scaling vectors of the queries in the workload were uniformly distributed. Scale vectors were integers ranging from 2 to 256. Per observations in practice, we assumed that both dimensions were coupled. We considered a storage space constraint of 35%, which is slightly higher than the additional storage space taken by image pyramids. The PRE-AGGREGATESSELECTION algorithm yields 12 pre-aggregates for this test where we executed scaling operations with scale vectors 2, 4, 6, 11, 15, 22, 32, 46, 67, 95, 137 and 182. The cost of computing the workload using these pre-aggregates is 18, 565. In contrast, image pyramids selects scaling operations with scale vectors: 2, 4, 8, 16, 32, 64, 128, and 256, and requires 33% additional storage space. Image pyramids computes the workload at a cost of 29, 166. The results of this experiment show that the pre-aggregates selected by our algorithm provide an improved performance for scaling operations over image pyramids. The cost of computing the workload using our algorithm is 36% less than that incurred by image pyramids, at a price of 2% additional storage space. Fig. 5.2(a) shows the distribution of the scale vectors of all queries in the workload. The pre-aggregates selected by image pyramids and our pre-aggregation selection algorithm are shown in Fig. 5.2(b) and 5.2(c), respectively. Poisson Distribution The workload for this experiment consisted of scaling operations where the scale vectors had a Poisson distribution, and the mean value of the scale vector equaled 50. The PRE-AGGREGATES-SELECTION algorithm yields 33 pre-aggregates for this test that executed scaling operations using scale vectors from 34 to 66. The cost of computing the workload using these pre-aggregates is 42, 455. In contrast, image pyramids
5.5 Experimental Results 87 (a) Query workload (Uniform distribution) (b) Selected queries for materialization by image pyramids (c) Selected queries for materialization by our pre-aggregation selection algorithm Figure 5.2. Query Workload with Uniform Distribution selects scaling operations with scale vectors: 2, 4, 8, 16, 32, 64, 128, and the cost of computing the workload is 95, 468. Thus, the cost of computing the workload using
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Applying OLAP Pre-Aggregation Techn
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Acknowledgments I would like to exp
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Abstract Large multidimensional arr
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Contents 1 Introduction and Problem
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List of Figures 2.1 3D Array . . .
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List of Tables 3.1 UNO and FAO Suit
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Chapter 1 Introduction and Problem
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Relevant and complementary question
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1.2 Publications Related to this Th
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Chapter 2 Background and Related Wo
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2.1 Array Databases 17 Figure 2.2 s
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2.1 Array Databases 19 toward the s
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2.1 Array Databases 21 • Bilinear
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2.1 Array Databases 23 given image
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2.2 On-Line Analytical Processing (
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2.3 Discussion 33 spatial-vector da
Page 41 and 42: 2.3 Discussion 35 • Both applicat
Page 43 and 44: Chapter 3 Fundamental Geo-Raster Op
Page 45 and 46: 3.2 Geo-Raster Operations 39 3.1.2
Page 47 and 48: 3.2 Geo-Raster Operations 41 multip
Page 49 and 50: 3.2 Geo-Raster Operations 43 Table
Page 51 and 52: 3.2 Geo-Raster Operations 45 turn i
Page 53 and 54: 3.2 Geo-Raster Operations 47 (a) Or
Page 55 and 56: 3.2 Geo-Raster Operations 49 Query
Page 57 and 58: 3.2 Geo-Raster Operations 51 contai
Page 59 and 60: 3.2 Geo-Raster Operations 53 is the
Page 61 and 62: 3.2 Geo-Raster Operations 55 3.2.4
Page 63 and 64: 3.2 Geo-Raster Operations 57 As in
Page 65 and 66: 3.2 Geo-Raster Operations 59 Local
Page 67 and 68: 3.3 Summary 61 Slicing The slicing
Page 69 and 70: Chapter 4 Answering Basic Aggregate
Page 71 and 72: 4.1 Framework 65 pre-aggregated res
Page 73 and 74: 4.2 Cost Model 67 By partitioning t
Page 75 and 76: 4.2 Cost Model 69 Cost of independe
Page 77 and 78: 4.3 Implementation 71 Algorithm 1 Q
Page 79 and 80: 4.4 Experimental Results 73 Query E
Page 81 and 82: 4.5 Summary 75 pre-aggregates: inde
Page 83 and 84: Chapter 5 Pre-Aggregation Support B
Page 85 and 86: 5.2 Conceptual Framework 79 Figure
Page 87 and 88: 5.2 Conceptual Framework 81 Benefit
Page 89 and 90: 5.4 Answering Scaling Operations Us
Page 91: 5.5 Experimental Results 85 Algorit
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Page 97 and 98: 5.5 Experimental Results 91 vectors
Page 99 and 100: 5.5 Experimental Results 93 root no
Page 101 and 102: 5.5 Experimental Results 95 Figure
Page 107 and 108: 5.6 Summary 101 we considered non-u
Page 109 and 110: Chapter 6 Conclusion One of the big
Page 111 and 112: 6.1 Future Work 105 more non-spatio
Page 113 and 114: Bibliography [1] Blakeley J. A., La
Page 115 and 116: BIBLIOGRAPHY 109 [22] Moon B., Vega
Page 117 and 118: BIBLIOGRAPHY 111 [47] ESRI Inc. Arc
Page 119 and 120: BIBLIOGRAPHY 113 [73] Stefanovic N.
Page 121: BIBLIOGRAPHY 115 [97] Kotidis Y. an
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