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

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100 5. Pre-Aggregation Support Beyond Basic Aggregate Operations scaling operations selected for pre-aggregation when c = 1.3%. For this instance of the storage space constraint, the algorithm selected 4 pre-aggregates shown in Table 5.4. The total cost of computing the workload is 3361. In contrast, computing the workload using the original dataset incurs a cost of 1.35e + 16. Table 5.2. ECHAM T-42 Climate Simulation Dimensions Dimension Extent Longitude 128 Latitude 64 Elevation 17 Time (24 min/slice) 200 years (2,190,000) Table 5.3. 4D Scaling: Scale Vector Distribution Scale Vector count 2,2,10,230 200 3,3,11,231 300 4,4,12,232 500 5,5,13,233 800 6,6,14,234 1000 7,7,15,235 1000 8,8,16,236 800 9,9,17,237 500 10,10,18,238 300 11,11,19,239 200 Table 5.4. 4D Scaling: Selected Pre-Aggregates Scale Vector count 2,2,10,230 200 4,4,12,232 500 6,6,14,234 1000 8,8,16,236 800 5.6 Summary This chapter describes our investigations on the problem of intelligently picking a subset of scaling operations given a storage space constraint. There is a tradeoff between the amount of space allocated for pre-aggregation, and the average query cost of scaling operations. We introduced a pre-aggregation selection algorithm based on a given query workload that determines a set of pre-aggregates in face of storage space constraints. We performed experiments on 2D, 3D, and 4D datasets using different data distribution patterns for the scale vectors. We relied on artificial data distributions since no empirical distributions were found. In addition to uniformly distributed scale vectors,
5.6 Summary 101 we considered non-uniform distributions including Poisson, peak, and step. For 2D datasets, we showed that our algorithm performs better than that of image pyramids. In particular, for non-uniform data distributions, our pre-aggregation selection algorithm not only provides a lower average query cost, but makes a much more efficient use of storage space. This is because our algorithm considers the frequency of the query, and the cost savings (benefit) this provides for computing the workload. Nevertheless, the major advantage of our algorithm over that of image pyramids is not the improved average query cost, but the reduced amount of storage space required for the pre-aggregates, especially for non-uniform distributions. In our experiments with 3D and 4D datasets, we showed the effect of the available storage space for pre-aggregation on average query costs. We observed that a small amount of storage overhead is sufficient to dramatically reduce average query costs. Since there are no similar techniques against which we can compare our results, we compared our results against the average query costs obtained by using the original data.
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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
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3.2 Geo-Raster Operations 43 Table
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3.2 Geo-Raster Operations 45 turn i
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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 and 100: 5.5 Experimental Results 93 root no
Page 101 and 102: 5.5 Experimental Results 95 Figure
Page 103 and 104: 5.5 Experimental Results 97 Figure
Page 105: 5.5 Experimental Results 99 Figure
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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