From GPS and Google Earth to Spatial ComputingFrom GPS and Google Earth to Spatial Computing

CSCI 5980 CSCI 5980

Team 3: Fan Zhang, Zhiqi ChenOct 24, 2012

Structures and Access Methods Structures and Access Methods Chapter 6Chapter 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.

Relevance to CourseRelevance 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.

Related Material in TextbookRelated 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.

Novelty in Encyclopedia ArticlesNovelty in Encyclopedia Articles

• Characteristics of R-tree

• Algorithms cover Range search, insertion, delete, and condense.

• R-tree Variants• R +-tree• R*-tree• Other variants

Societal MotivationSocietal 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

Computer Science MotivationComputer 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.

R-TreeR-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.

R-TreeR-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