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

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4 Answering Basic Aggregate Queries Using Pre-Aggregated Data 63 4.1 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1.1 Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.1.2 Pre-Aggregation . . . . . . . . . . . . . . . . . . . . . . . . 64 4.1.3 Aggregate Query and Pre-Aggregate Equivalence . . . . . . . 64 4.2 Cost Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.1 Computing Queries from Raw Data . . . . . . . . . . . . . . 68 4.2.2 Computing Queries from Independent and Overlapped Pre- Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.3 Computing Queries from Dominant Pre-Aggregates . . . . . 69 4.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5 Pre-Aggregation Support Beyond Basic Aggregate Operations 77 5.1 Non-Standard Aggregate Operations . . . . . . . . . . . . . . . . . . 77 5.2 Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2.1 Lattice Representation . . . . . . . . . . . . . . . . . . . . . 79 5.2.2 Pre-Aggregation Selection Problem . . . . . . . . . . . . . . 80 5.3 Pre-Aggregates Selection . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3.1 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . 83 5.4 Answering Scaling Operations Using Pre-Aggregated Data . . . . . . 83 5.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.5.1 2D Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5.2 3D Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.5.3 4D Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6 Conclusion 103 6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
List of Figures 2.1 3D Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Map Algebra Functions . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Image Tiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 Image Pyramids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Nearest Neighbor, Bilinear and Cubic Interpolation Methods . . . . . 22 2.6 3D Scaling Operations on Time-Series Imagery Datasets . . . . . . . 24 2.7 OLAP Data Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.8 Typical OLAP Cube Operations . . . . . . . . . . . . . . . . . . . . 27 2.9 OLAP Approaches: MOLAP, ROLAP, and HOLAP . . . . . . . . . . 27 2.10 MOLAP Storage Scheme . . . . . . . . . . . . . . . . . . . . . . . . 28 2.11 ROLAP Storage Scheme . . . . . . . . . . . . . . . . . . . . . . . . 29 2.12 Typical Query as Expressed in ROLAP and MOLAP Systems . . . . 29 2.13 Star Model of a Spatial Warehouse . . . . . . . . . . . . . . . . . . . 32 2.14 Comparison of Roll-Up and Scaling Operations . . . . . . . . . . . . 34 3.1 Reduction of Contrast in the Green Channel of an RGB Image . . . . 40 3.2 Highlighted Infrared Areas of an NRG Image . . . . . . . . . . . . . 41 3.3 Cells of Rasters A and B with Equal Values . . . . . . . . . . . . . . 42 3.4 Re-Classification of the Cell Values of a Raster Image . . . . . . . . . 43 3.5 Computation of a Proximity Operation . . . . . . . . . . . . . . . . . 44 3.6 Computation of an Overlay Operation . . . . . . . . . . . . . . . . . 45 3.7 Computation of an Overlay Operation Considering Values Greater than Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.8 Calculation of the Total Sum of Cell Values in a Raster . . . . . . . . 47 3.9 Result of an Average Aggregate Operation . . . . . . . . . . . . . . . 48 3.10 Result of a Maximum Aggregate Operation . . . . . . . . . . . . . . 48 3.11 Result of a Minimum Aggregate Operation . . . . . . . . . . . . . . 49 3.12 Computation of the Histogram for a Raster Image . . . . . . . . . . . 50 3.13 Computation of the Diversity for a Raster Image . . . . . . . . . . . . 50 3.14 Computation of a Majority Operation for a Raster Image . . . . . . . 51 3.15 Computation of the Variance for a Raster Image . . . . . . . . . . . . 52 3.16 Computation of the Standard Deviation for a Raster Image . . . . . . 52 3.17 Computation of Median for a Raster Image . . . . . . . . . . . . . . 54 3.18 Computation of a Top-k Operation for a Raster Image . . . . . . . . . 54 3.19 Computation of a Translation Operation for a Raster Image . . . . . . 56 5
Page 1: Applying OLAP Pre-Aggregation Techn
Page 5 and 6: Acknowledgments I would like to exp
Page 7 and 8: Abstract Large multidimensional arr
Page 9: Contents 1 Introduction and Problem
Page 13 and 14: List of Tables 3.1 UNO and FAO Suit
Page 15 and 16: Chapter 1 Introduction and Problem
Page 17 and 18: Relevant and complementary question
Page 19 and 20: 1.2 Publications Related to this Th
Page 21 and 22: Chapter 2 Background and Related Wo
Page 23 and 24: 2.1 Array Databases 17 Figure 2.2 s
Page 25 and 26: 2.1 Array Databases 19 toward the s
Page 27 and 28: 2.1 Array Databases 21 • Bilinear
Page 29 and 30: 2.1 Array Databases 23 given image
Page 31 and 32: 2.2 On-Line Analytical Processing (
Page 39 and 40: 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
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3.2 Geo-Raster Operations 55 3.2.4
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3.2 Geo-Raster Operations 57 As in
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3.2 Geo-Raster Operations 59 Local
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3.3 Summary 61 Slicing The slicing
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Chapter 4 Answering Basic Aggregate
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4.1 Framework 65 pre-aggregated res
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4.2 Cost Model 67 By partitioning t
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4.2 Cost Model 69 Cost of independe
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4.3 Implementation 71 Algorithm 1 Q
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4.4 Experimental Results 73 Query E
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4.5 Summary 75 pre-aggregates: inde
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Chapter 5 Pre-Aggregation Support B
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5.2 Conceptual Framework 79 Figure
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5.2 Conceptual Framework 81 Benefit
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5.4 Answering Scaling Operations Us
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5.5 Experimental Results 85 Algorit
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5.5 Experimental Results 87 (a) Que
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5.5 Experimental Results 89 (a) Sel
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5.5 Experimental Results 91 vectors
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5.5 Experimental Results 93 root no
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5.5 Experimental Results 95 Figure
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5.6 Summary 101 we considered non-u
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Chapter 6 Conclusion One of the big
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6.1 Future Work 105 more non-spatio
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Bibliography [1] Blakeley J. A., La
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BIBLIOGRAPHY 109 [22] Moon B., Vega
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BIBLIOGRAPHY 111 [47] ESRI Inc. Arc
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BIBLIOGRAPHY 113 [73] Stefanovic N.
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BIBLIOGRAPHY 115 [97] Kotidis Y. an
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