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

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94 5. Pre-Aggregation Support Beyond Basic Aggregate Operations Figure 5.11. Selected Pre-Aggregates, c = 36% Uniform distribution in x, y and Poisson distribution in t In this experiment, the workload consisted of 23, 460 scaling operations referring to 3D dataset R2. The scale vectors were uniformly distributed along x and y, with a Poisson distribution along t. Values of scale vectors ranged from 2 to 256 in the x and y dimensions, whereas in t they ranged from 8 to 16, with a mean value of 12. Fig. 5.12 shows the distribution of scaling vectors in the workload. Note that the scale vector values in the dimensions x and y are coupled. The frequency of the various scale factor values is denoted by f. We ran the PRE-AGGREGATESSELECTION algorithm for different values of the storage space constraint. The minimum storage space required to support the root node of the lattice was 3.13% of the size of the original dataset. Fig. 5.13 shows the average query cost as storage space increases. A small amount of storage space dramatically improves the average query cost. However, we can also observe that the improvement in average query cost decreases as allocated space goes beyond 26%. Fig. 5.14 shows the scaling operations selected for pre-aggregation when c = 26%. For this instance of the storage space constraint, the algorithm selected 67 pre-aggreagates. The total cost for computing the workload is 1.21e + 07. In contrast, computing the workload using the original dataset incurs a cost of 2.31e + 11. Poisson distribution in x, y, t In this experiment, the workload consisted of 600 scaling operations referring to 3D dataset R2. The scale vectors followed a Poisson distribution along the three dimensions x, y, and t. Values of scale vectors ranged from 2 to 10 in the x and y dimensions, whereas in t they ranged between 8 and 16, with a mean value of 12. Fig. 5.15 shows the distribution of the scaling vectors in the workload. We ran the PRE-AGGREGATESSELECTION algorithm for different values of the storage space
5.5 Experimental Results 95 Figure 5.12. Workload with Uniform Distribution Along x, y, and Poisson distribution in t Figure 5.13. Average Query Cost as Space is Varied constraint. The minimum storage space required to support the root node of the lattice was 4.18% of the size of the original dataset. Fig. 5.16 shows the average query cost as storage space is increased. A small amount of storage space dramatically improves the average query cost. However, the improvement in average query cost decreases as allocated space goes beyond 26%. Fig. 5.17 shows the scaling operations selected for pre-aggregation when c = 30%. For this instance of the storage space constraint, the algorithm selected 23 pre-aggreagates. The total cost of computing the workload is 1680. In contrast, computing the workload using the original dataset incurs a cost of 1.34e + 12.
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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
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2.3 Discussion 35 • Both applicat
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Chapter 3 Fundamental Geo-Raster Op
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3.2 Geo-Raster Operations 39 3.1.2
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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 and 92: 5.5 Experimental Results 85 Algorit
Page 93 and 94: 5.5 Experimental Results 87 (a) Que
Page 95 and 96: 5.5 Experimental Results 89 (a) Sel
Page 97 and 98: 5.5 Experimental Results 91 vectors
Page 99: 5.5 Experimental Results 93 root no
Page 103 and 104: 5.5 Experimental Results 97 Figure
Page 105 and 106: 5.5 Experimental Results 99 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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