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32 2. Background and Related Work relation. When the base relation affects more than one materialized view, multiple maintenance expressions must be evaluated. Multi-query optimization techniques can be used to detect common sub-expressions between the maintenance expressions so that an efficient global evaluation plan for the maintenance expressions can be achieved [61, 62]. Numerous methods have been developed for materialized view maintenance in conventional database systems. Zhuge et al. [101] introduced the Eager Compensating Algorithm (ECA) based on previous incremental view maintenance algorithms and compensating queries used to eliminate anomalies. In [102], authors define multiple views consistent with each other as the multiple view consistency problem. Further research from the same authors [102, 103] considers data warehouse views defined on base tables located in different data sources, i.e., if a view involves n base tables, then n data sources are also involved. A common characteristic of the early approaches to view maintenance is the considerable need for accessing base relations, which in most cases results in performance degradation. The improvement of the efficiency of view maintenance techniques has been a topic of active research in the database research community [15, 65, 85, 98]. Spatial OLAP (SOLAP) The multidimensional approach used by data warehouses and OLAP does not support array data types or spatial data types such as point, lines, or polygons. Following the development trends of data warehouse and data mining techniques, Stefanovic et al. [52] proposed the construction of a spatial data warehouse to enable on-line data analysis in spatial-information repositories. The authors used a star/snowflake model to build a spatial data cube consisting of both spatial and non-spatial dimensions and measures: the data cube shown in Fig. 2.13 consists of one spatial dimension (region) and three non-spatial dimensions (precipitation, temperature, and time). Figure 2.13. Star Model of a Spatial Warehouse Current research in spatial data management focuses on querying spatial data, particularly regarding the improvement of aggregate query performance [57] for
2.3 Discussion 33 spatial-vector data structures. Alas, little attention has been given to spatial-raster data [42, 73, 86]. Support for spatial-raster data typically consists of creating a spatial-raster cube from information in the metadata file (such as size, level, width, height, date of creation, format, and location) [28, 94]. Vega et al. [40] presented a model to analyze and compare existing techniques for the evaluation of aggregate queries on spatial, temporal, and spatio-temporal data. The study shows that existing aggregate computation techniques rely on some form of pre-aggregation and support is restricted to distributive aggregate functions such as COUNT , SUM, and MAX. Additionally, the authors identify several important needs concerning aggregate computation. First, they discuss the need to develop further and more substantial techniques to support holistic aggregate functions e.g., MEDIAN, RANK, and to better support selective predicates. The second observation pertains to the lack of support for queries needing to be efficiently evaluated at every granule in time. Existing aggregate computation techniques focus only on spatial objects such as lines, points, and polygons but do not consider aggregate computation on data grids (array) structures. 2.3 Discussion Query performance is a major concern underlying the design of databases in both business and remote-sensing imaging applications. While there are some valuable research results in the realm of pre-aggregation techniques to support query processing in business and statistical applications, little has been done in the field of array databases. The question therefore arises, what distinguishes array data from traditional data types that it cannot be fully supported by relational databases and thus take advantage of advance technologies such as OLAP? OLAP from its very conception was designed to assist in the decision-making process of business applications, where business perspectives such as products and/or stores, represented the dimensions of the data cube. And while the different columns in a data cube are usually called dimensions, they generally cannot be considered as a special extent of the entities modeled by the database. Instead, they are regarded as explicit attributes that characterize a particular entity. Some dimensions in a data cube (e.g., CustomerId) are defined over discrete domains which do not have a natural ordering among their values (customer 1000 cannot be considered close to customer 1001). In such cases, any ordering defined for the values in one of these columns is arbitrary [40]. For this reason, existing OLAP solutions and related pre-aggregation techniques cannot be applied to multidimensional arrays, at least not in a straight-forward manner. Recently, however, a new trend in OLAP gained considerable popularity due to its capabilities to support Geo-spatial data. Spatial OLAP considers the case in which a data-cube may have both spatial and non-spatial dimensions. However, spatial OLAP focuses mainly on spatial-vector data and so far little support has been provided for spatial-raster data in terms of selective materialization for the optimization of aggregates. Support is limited only to those operations that can be constructed from
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
Page 31 and 32: 2.2 On-Line Analytical Processing (
Page 37: 2.2 On-Line Analytical Processing (
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 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
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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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