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

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24 2. Background and Related Work (a) 3D dataset (b) 3D dataset (scaled-down along dim1 and dim2 by a factor of 2) (c) 3D dataset (scaled-down along dim3 by a factor of 4) (d) 3D dataset (scaled-down along all dimensions by a factor of 2) Figure 2.6. 3D Scaling Operations on Time-Series Imagery Datasets
2.2 On-Line Analytical Processing (OLAP) 25 2.1.7 Summary Array database theory is gradually entering its consolidation phase. The notion of arrays as functions mapping points of some hypercube-shaped domain to values of some range set is commonly accepted. Two main modeling paradigms are used: calculus and algebra. Multidimensional data models embed arrays into the relational world, either by providing conceptual stubs like Array Algebra, or by adding relational capabilities explicitly such as AQL and RAM. Notably, aggregate query processing plays a critical role given the large volumes of the arrays. Our study shows that pre-aggregation techniques focus only on 2D datasets, and that support is limited to one particular operation: scaling. We distinguish the pyramid approach as the most popular method for speeding up scaling operations on 2D datasets; despite its known limitations such as hard-wired interpolation and lack of support for datasets of higher dimensions. Advances on hardware graphics are enabling quicker and more accurate visualization and navigation capabilities for raster imagery. However, little work has been reported on how array database technology is progressively exploiting these hardware advances. A critical gap with respect to pre-aggregation is the lack of support for aggregate operations other than 2D scaling. 2.2 On-Line Analytical Processing (OLAP) Data warehousing/OLAP is an application domain where complex multidimensional aggregates on large databases have been studied intensively. Typically, a data warehouse collects business data from one or multiple sources so that the desired financial, marketing, and business analyses can be performed. These kinds of analyses can detect trends and anomalies, make projections, and make business decisions [41]. When such analysis predominantly involves aggregate queries, it is called on-line analytical processing, or OLAP [38, 39]. To understand the mechanism of pre-computation, the following subsections review different approaches to structuring multidimensional data, storage mechanisms and operations in OLAP. 2.2.1 OLAP Data model The multidimensional OLAP model begins with the observation that the factors that influence decision-making processes are related to enterprise-specific facts, such as sales, shipments, hospital admissions, surgeries, and so on. [68]. Instances of a fact subsequently correspond to events that occur. For example, every sale or shipment carried out is an event. Each fact is described by the values of a set of relevant measures providing quantitative descriptions of events, e.g., sales receipts, amounts shipped, hospital admission costs, and surgery times are all measures. In OLAP, information is viewed conceptually as cubes that consist of descriptive categories (dimensions) and quantitative values (measures) [26, 81, 69, 83]. In the scientific literature, measures are at times called variables, metrics, properties, attributes, or indicators. Figure 2.7 illustrates a 3D OLAP data cube where business events
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
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Page 39 and 40: 2.3 Discussion 33 spatial-vector da
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Page 67 and 68: 3.3 Summary 61 Slicing The slicing
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Page 71 and 72: 4.1 Framework 65 pre-aggregated res
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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
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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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