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

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26 2. Background and Related Work (facts) are mapped at the intersection of a specific combination of dimensions. Different attributes along each dimension are often organized in hierarchical structures that determine the different levels in which data can be further analyzed [26]. For example, within the time dimension, one may have levels composed of years, months, and days. Similarly, within the geography dimension, one may have levels such as country, region, state/province, or city. Hierarchical structures are used to infer summarization (aggregation), that is, whether an aggregate view (query) defined for some category can be correctly derived from a set of precomputed views defined for other categories. Figure 2.7. OLAP Data Cube 2.2.2 OLAP Operations OLAP includes a set of operations for manipulation of dimensional data organized in multiple levels of abstraction. Basic OLAP operations are roll-up, drill-down, slice, dice and pivot [44]. A roll-up (aggregation) operation computes higher aggregations from lower aggregations or base facts according to their hierarchies, whereas drilldown (disaggregation) is an analytic technique whereby the user navigates among levels of data ranging from most summarized/aggregated, to most detailed. Typical OLAP aggregate functions include average, maximum, minimum, count, and sum. Drilling paths may be defined by the hierarchies within dimensions or other relationships dynamic within or between dimensions. A slice consists of the selection of a smaller data cube or even the reduction of a multidimensional data cube to fewer dimensions by a point restriction in some dimension. The dice operation works similarly to the slice except that it performs a selection on two or more dimensions. Figure 2.8 provides a graphical description of these operations. 2.2.3 OLAP Architectures Figure 2.9 shows different approaches for the implementation of OLAP functionalities: Multidimensional OLAP (MOLAP), Relational OLAP (ROLAP), Hybrid OLAP
2.2 On-Line Analytical Processing (OLAP) 27 Figure 2.8. Typical OLAP Cube Operations (HOLAP). These approaches offer a common view in the form of data cubes, which are independent of how the data is stored. Figure 2.9. OLAP Approaches: MOLAP, ROLAP, and HOLAP MOLAP MOLAP maintains data in a multi-dimensional matrix based on a non-relational specialized storage structure [37], see Fig. 2.10(a). While building the storage structure, selected aggregations associated with all possible roll-ups are precomputed and stored [92]. Thus, roll-up and drill-down operations are executed in interactive time. Products such as Oracle Essbase, IBM Cognos Powerplay, and open-source Palo have adopted this approach. A MOLAP system is based on an ad-hoc logical model that directly represents multidimensional data and its applicable operations. The underlying multidimensional database physically stores data as arrays and access to it is positional [68]. Grid-files [53, 55], R*-trees [71] and UB-trees [84] are among the techniques used for that purpose. The main advantage of this approach is that it contains the pre-computed aggregate values that offer a very compact and efficient way to retrieve answers for specific
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 and 10: Contents 1 Introduction and Problem
Page 11 and 12: List of Figures 2.1 3D Array . . .
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
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Page 39 and 40: 2.3 Discussion 33 spatial-vector da
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Page 43 and 44: Chapter 3 Fundamental Geo-Raster Op
Page 45 and 46: 3.2 Geo-Raster Operations 39 3.1.2
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Page 55 and 56: 3.2 Geo-Raster Operations 49 Query
Page 57 and 58: 3.2 Geo-Raster Operations 51 contai
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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
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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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