Spatial Access Methods

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Spatial Access Methods Query Processing

• Matei Lunca Geographic Information Analysis
  2004
• Richardson Van Oosterom - Advances In Spatial
  Data Handling

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Inhoud

• Extend RDMS for GIS/GIA
• Trees
• Query types
• The curse of dimensionality
• Approximate matches

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Geographic Information Retrieval

• Spatial Access Methods
• Algoritmes voor opslaan en vinden van ruimtelijke
  gegevens 3-D met sterke relatie en dus niet via
  gewone structuren zoals B-Trees op te slaan
• Query Processing
• Datastructuur en DB zoekacties in deze context
• GIS vragen zoals buffer rond rivier

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Extending RDMS for GIS/GIA

• In GIS objects organized by location and
  extension in space
• Because of arbitrary complexity of spatial
  objects access methods for 2D objects such as
  minimum bounding rectangles needed
• Curse of dimensionality!

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Requirements of spatial access methods

• Dynamic
• Random access and queries must be supported
• Space efficient
• Complex spatial data can in many cases not be
  partitioned because of relations between objects,
  thus data blocks may be large and not fit In
  memory
• Efficiency independent of operators/ distribution
• For multiple DB storing different types of data
  to be joined
• Compatible with concurrency

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Practical requirements

• Costs of computing and communicating data
• Minimize external access costs (I/O)
• Indexing Trees
• Pointers at leaves/nodes
• Searching going down tree
• Fast for range queries
• Hashing address buckets
• No ordering needed

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Challenges in Indexing

• Most DB support
• B-Trees
• Hash tables
• Few DB support
• R-Trees
• Region quadtree
• Why is implementation so difficult?
• Integration with query optimizer
• Providing query operators that utilize the index
• Cost model (efficiency known before
  implementation)
• Concurrency control and recovery techniques

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Space Driven VS Data Driven

• Space Driven Trees
• Decomposition independent from data insertion
  order
• Region quadtree
• Data Driven Trees
• Space decomposed based on input data
• Point quadtree
• K-D Tree

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Space/Data Driven Structures

• Space driven structures Grids
• Twin grid file
• Shuffles points between the primary and secondary
  file to minimize the total size
• Multilayer grid file
• Uses two or more grid files, storing objects in
  the first grid file where no splitting across
  hyperplanes is needed
• Data driven structures - R-Tree

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Trees

• X-Tree
• TR-Tree
• IQ, PX MDX-Trees
• PX-Tree
• TV-Tree
• VAM-Split Trees

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Trees X-Tree

• Adapts R-Trees to high dimensional data
• Overlap-free split based on split history
• R/R-Trees lead to high overlap
• diminish advantages of hierarchical partitions
• When algorithm would lead to unbalanced directory
  the X-Tree omits the split and the node becomes a
  super node
• Supernodes are nodes enlarged by a multiple of
  the block size that avoid splits that would
  result in an inefficient structure by linear
  scanning

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Trees X-Tree (2)

• Dynamically use overlap-minimizing splits
• Supernodes accessed sequentially if no good split
  decision found for a directory node

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Trees TR-Tree

• Improved R-Tree
• Represent exact geometry spatial attributes
• Reduce memory operations
• Store components of 1 decomposed object
• Internal node
• Pointer child node
• Minimum bounding rectangle of trapezoids in child
• Leaf node
• Trapezoids

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Trees TR-Tree (2)

• Representation of Bavaria

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Trees IQ-, PX- MDX-Trees

• IQ-Tree
• Index structure for query processing in
  high-dimensional data spaces
• Compresses data to improve query processing
• PX-Tree Multi-Disc X-Tree
• Parallel access method
• Short response time high query throughput

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Trees TV-Tree

• R-Tree-like varying length feature vector
• Telescope vector
• Divide attributes into
• Those common to all subtree items
• Those used for branching
• Those ignored
• Knowledge about the behaviour of single
  attributes (their selectivity) is necessary

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Trees VAM-Split Trees

• VAM-Split R-Tree
• VAM-Split KD-Tree
• Static index structures
• All objects must be available when index is
  created
• Splits are performed at maximum variance value
• Built in memory before permanently stored on disk
• Size limited to the amount of (virtual) memory
  available

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Other Trees

• The Cell Tree
• Levels of data split by arbitrary hyperplanes
• Concave objects decomposed into convex pieces,
  which are indexed in every cell that they overlap
• The K-D Tree
• Levels of data are split along different
  dimensions into non-overlapping cells
• Objects indexed in all cells they intersect

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Other Trees (2)

• Generalized BD Tree
• Stores objects as hierarchy of minimum bounding
  boxes
• The P-Tree
• Hyperplanes split space hierarchically by
  polytopes
• multidimensional boxes with nonrectangular
  sides
• R-Tree special case in which all polytopes are
  boxes
• R-files
• Divide space into hierarchy of nested boxes in
  which objects are indexed in lowest cell which
  contains them

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Cost Models

• Curse of dimensionality performance
  deteriorations
• Cost model for query processing in
  high-dimensional data spaces for careful
  optimization of parameters of an index
• Data space quantization
• Data compression - VA File, IQ Tree
• Reduce I/O by representing attributes in less
  bits
• Page size
• Dimension assignment

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High-dimensional data spaces massive data sets

• Exotic data, cardinality/dimensionality
• Terabyte, petabyte
• Common problem overfit the data
• Common challenge fit model/pattern robustly
• Compression, statistics, stochastic analysis,
  discrete mathematics, harmonic analysis
• Complexity noisiness lead to constructing
  statistical/fuzzy models

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The Pyramid-Technique

• Maps data from D-dimensional space to 1D so
  B-Trees can be used to manage data
• Data space is divided into 2D pyramids
• Pyramids partitioned into data pages of B-Tree
• No inverse transformation needed because data and
  D-dimensional key stored

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The Pyramid-Technique (2)

• Complex queries
• Pyramid value calculated from query input
• Querying the tree with this value
• Result D-dimensional points sharing pyramid
  value that must be scanned for the search item
• Efficient query processing only in lt 8 D

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Query processing

• Direct VS indirect spatial search
• Direct locating objects in an geographical area
• Indirect queries based on non-spatial
  attributes
• Show geography complying non-spatial requirements

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Query processing steps

• Query input
• Filter step
• Spatial index
• Candidate set
• Refinement step
• Load spatial extent
• Test spatial extent
• Hits/false drops
• Query result output

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Graphical Query Example
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Graphical Query Example
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Query types

• Point query/point-in-polygon query
• Parameter coordinates
• What objects exists at these coordinates?
• Window/range query
• Parameter region defined by coordinates
• What objects are located in this region?
• Distance and Buffer Zone queries
• Parameters buffer object and distance
• What objects are there within given distance from
  buffer?

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Query types (2)

• Path queries (network structure required)
• Parameters network locations
• What is the shortest route from A to B?
• Join and Range queries
• Spatial objects and relationships
• Spatial predicates points, windows, buffers,
  paths
• Overlaying roads and waterworks GIS layers and
  displaying the result according to relative
  height (river, bridge, aqueduct) is a spatial join

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Query types (3)

• Feature approach feature vectors
• Neighborhood search
• Spatial-Query-by-Sketch
• Multimedia (2D) search instead of alphanumeric

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Spatial-Query-by-Sketch Sketcho 1.1b
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Spatial-Query-by-Sketch Sketcho 1.1b
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Spatial-Query-by-Sketch Sketcho 1.1b
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Spatial-Query-by-Sketch Sketcho 1.1b
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Similarity search

• Approximate surface
• by parametric functions
• Assigning appropriate
• class to query object
• Section Coding each polygons circumcircle is
  decomposed into sectors normalized
• Similarity distance feature vectors

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Similarity search (2)

• Shape Histograms (feature vectors!)
• Bins complete disjoint cells of space
• Shell Model
• Concentric uniform shells around the center
• Independent of rotation around the center
• Sector Model
• Distribute uniformly on surface (Voronoi)

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Shape Histograms
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Special Query Types

• Spatial continuous queries
• In dynamic environments continuous pooling
  necessary, because otherwise query results
  meaningless
• Result, expiry time given current motion vector,
  and change that can cause expiration
• Spatio-temporal queries
• Spatiotemporal Database Systems (STDBS) track and
  presenting data about moving objects, such as GPS
• Probabilistic models are also available that
  attempt to plot future values in order to give
  faster response

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Query pre-processing

• Pre-optimize index structure
• With specific knowledge if we use a TIN for
  river network studies, valleys are more important
  and could be stored at high nodes in tree
• Avoid characteristic areas dont store exact
  geometry of a chasm, but no-go denomination

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Query processing strategies

• Parallel searches (nice split)
• In varying data structures
• Shape-based strategy
• Models the direction region
• Converts processing of direction predicates into
  processing of topological operations between open
  shapes and closed geometry objects
• Eliminates computation related to world boundary

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Approximate Search/Match
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Screenshots - LTRMP
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Hoofdpunten

• Spatial context definieren/representeren
• Space Driven VS Data Driven
• Ieder toepassing zijn eigen techniek
• Approximate/Fuzzy approach
• Tree
• Hashing
• 3D histogram