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From GPS and Google Earth to Spatial Computing CSCI 5980

From GPS and Google Earth to Spatial Computing CSCI 5980. Team 3: Fan Zhang, Zhiqi Chen Oct 24, 2012. Structures and Access Methods Chapter 6. Encyclopedia Articles Voronoi Diagram, J. Kang, page 1232-1235.  R-tree, M. Hadjieleftheiou, et al, page 993-1002. 

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From GPS and Google Earth to Spatial Computing CSCI 5980

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  1. From GPS and Google Earth to Spatial ComputingCSCI 5980 Team 3: Fan Zhang, Zhiqi Chen Oct 24, 2012

  2. Structures and Access Methods Chapter 6 Encyclopedia Articles • Voronoi Diagram, J. Kang, page 1232-1235.  • R-tree, M. Hadjieleftheiou, et al, page 993-1002.  • R*-tree, H. Kriegel, P. Kunath, page 987-992.  • Mobile Object Indexing, G. Kollios, V. Tsotras, page 663-670. 

  3. Relevance to Course • Voronoi Diagram: The method decomposes a set of objects in a spatial space to a set of polygonal partitions. • R-tree: It is a hierarchical data structure based on B+-tree, used for dynamic organization of a set of d-dimensional geometric objects. • R*-tree: An improvement of the R-tree. Popular access method for points and rectangles. • Mobile Object Indexing: Supplement content in the textbook.

  4. Related Material in Textbook 6.6 Collections of objects • Rectangles and minimum bounding boxes(MBB) • MBB, the smallest bounding rectangle with sides parallel to the axes of the Cartesian frame. • R tree • A way of indexing rectangles. • Each node represents a rectangle. • The leaf nodes represent the actual rectangles to be indexed. • R +-tree • No overlapping rectangles associated with non-leaf nodes. • Improve the efficiency of point and range queries.

  5. Novelty in Encyclopedia Articles • Characteristics of R-tree • Algorithms cover Range search, insertion, delete, and condense. • R-tree Variants • R +-tree • R*-tree • Other variants

  6. Societal Motivation • Voronoi diagram • Sciences, Astronomy, Biology, Forestry, Geology, Medicine, Spatial Data, Geography. Graph Theory, Nearest Neighbor Problem, Route Planning • R-Trees • Spatial data management, p2p system, data streams, bio-informatics, all aspects concerning a database system • R*-Tree • Geographic Information Systems(GIS), Digital Mock-up(DMU), Multidimensional Feature Vectors • Mobile object indexing • Traffic monitoring, intelligent navigation, mobile communications management

  7. Computer Science Motivation • R*-Tree • Improvement of R-tree • Popular access methods for points and rectangles • Modifying the insert and split algorithms of R-tree • Supports point and spatial data at the same time • Implementation cost is slightly higher than that of other R-tree variants • Mobile Object Indexing • An object’s movement can be presented through a linear function of time with their initial location, a starting tune instant and a velocity vector.

  8. R-Tree Characteristics of R-Tree • The root node of the tree contains at least two entries. • Every internal node contains a set of rectangles and pointers to the corresponding child node. • Every leaf node contains the rectangles of spatial objects. • Nodes are guaranteed half full. • The R-tree is a height-balanced structure.

  9. R-Tree The R-tree range search algorithm RangeSearch(TypeNode RN, TypeRegion Q) /* Finds all rectangles that are stored in an R-tree with root node RN, which intersect with a query rectangle Q. Answers are stored in set A. */ if RN is not a leaf node examine each entry e of RN to find e.mbb that intersect Q; foreach such entry e call RangeSearch(e.p, Q); else // RN is a leaf node examine each entry e to find e.mbb  that intersects Q; add these entries to answer set A; endif

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