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

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66 4. Answering Basic Aggregate Queries Using Pre-Aggregated Data ✷ DPAS := {p 1 , p 2 , . . . , p n | Q .sdom ⊆ p i.sdom } . (4.4) Moreover, given an ordered DPAS DPAS = {p 1 , p 2 , . . . , p n | Q .sdom ⊆ p 1.sdom ⊆ . . . ⊆ p n.sdom } , (4.5) the closest dominant pre-aggregate (p cd ) to Q is given by p 1 , i.e., p cd = p 1 . (a) Independent preaggregate (b) Overlapped preaggregate (c) Dominant preaggregate Figure 4.1. Types of Pre-Aggregates Cases may occur where a pre-aggregate intersects with one or more pre-aggregates of the same or different type. Intersections are problematic because the greater the number of intersections, the greater the number of cells that may need to be computed from raw data to determine the real contribution towards the result of the query by a given pre-aggregate. The computation process involves several intermediary operations such as decomposing the pre-aggregate into sub-partitions that in turn must be aggregated. Moreover, the same procedure must be performed on the other intersected pre-aggregates should we want to use their results. For example, assume that pre-aggregates p 1 , p 2 and p 3 can be used to answer query Q, and that they all intersect with each other. Since the result of each pre-aggregate includes a partial result of the other two pre-aggregates, we must use raw data to compute the intersected area and adjust the result of the pre-aggregate according to the aggregate function specified in the query predicate. To overcome this problem, a query selected for pre-aggregation for which other pre-aggregates exist with different spatial domains but identical structural properties can be decomposed into a set of sub-partitions prior to the pre-aggregation process.
4.2 Cost Model 67 By partitioning the query to be pre-aggregated we can avoid intersection among preaggregates, see example shown in Fig. 4.2. Figure 4.2. Selected Queries for Pre-Aggregation (left) and Decomposed Queries (right) 4.2 Cost Model This section introduces a cost model that allows us to estimate the cost (in terms of execution time) of computing a query using pre-aggregates compared to raw data. In our model, the access cost is driven by the number of required disk I/Os and memory accesses. These parameters are influenced by the number of tiles needed to answer a given query and the number and size of the cells in the datasets. The following assumptions underlie our estimates. 1. We assume that the tiles needed to answer a given query are stored using implicit storage of coordinates, which is the prevalent storage format for raster image data [79]. Implicit storage of coordinate values is a storage technique that leads to a higher degree of clustering of cell values that are close in data space, that is, it preserves spatial proximity of cell values. Given that state-of-the-art disk drives improve access to multidimensional datasets by allowing the spatial locality of the data to be preserved in the disk itself [93], we assume that it takes the same time to retrieve a tile from disk as to retrieve any other tile needed to answer a given query. Clearly, there are other factors, not considered here, that influence access cost. Among them are the cost for storing intermediate results, and the communication cost for sending the results from the client to the server. More complicated cost models are certainly possible, but we believe the cost
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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
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
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: 4.1 Framework 65 pre-aggregated res
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 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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