File Processing : Multi-dimensional Index

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File Processing Multi-dimensional Index

• 2008, Spring
• Pusan National University
• Ki-Joune Li

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Multi-Dimensional Index

• Multi-Attributes Query vs. Single Attribute Query
• Single Attribute Only ONE attribute to specify
  query condition
• Example Find Students whose record is in 3.5,
  4.5
• Multi-Attributes Several attributes
• Example Find students whose height is greater
  than 180 cm and weight is less
  than 70 Kg
• Each attribute corresponds to a dimension
• Multi-Attribute Query Multi-Dimensional Query

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Processing Multi-dimensional Queries

• Example Find students whose height gt 180 cm and
  weight lt
  70 Kg
• Method 1 Using a B-tree
• Step 1 Apply B-tree to search student taller
  than 180 cm
• Step 2 Search students lighter than 70 Kg
  from the result of step 1
• Height and Weight or Weight and Height ?

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Processing Multi-dimensional Queries

• Method 2 Using Two B-trees
• Step 1 Result1 ? Students taller than 180 cm by
  B-tree
• Step 2 Result2 ? Students lighter than 70 Kg by
  B-tree
• Step 3 Result ? Result1 ? Result2
• Comparison of Method 1 and Method 2

?
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Processing Multi-dimensional Queries

• Method 3 Unified Index for Several Attributes
• One index for several attributes
• Multi-Dimensional Space
• Two approaches
• Extending B-tree
• Extending Dynamic Hashing

Weight
Height
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Extending Hashing Grid Approach
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Extending Hashing Grid File
Directory
(x1, y1)
(x2, y2)
Block Pointer
Query
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Problem 1 Dead Space
No objects in this query area
5 block accesses
Query
Dead Space? Empty space with no objects
How to reduce dead space
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Minimum Bounding Rectangle
MBR(Minimum Bounding Rectangle)
Query
Only 1 Disk Access
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Problem 2 Non-Point Object
Where to store this object
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Minimum Bounding Rectangle

• MBR (Minimum Bounding Box)
• Two dimensional geometric simplification of
  objects
• Not the Whole space,
• only in the region occupied by objects

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Extending B-tree R-tree

• B-tree vs. R-tree
• B-tree Interval (1-D rectangle)
• R-tree Multi-Dimensional Interval (Rectangle)
• R-tree Rectangle B-tree
• Each Node
• MBR (Minimum Bounding Rectangle) instead of
  Interval (or Delimiter)
• No Linked-List for External Nodes
• A certain amount of overlapping is indispensable

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Extending B-tree R-tree

• Example

Root
Query
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Upward Split like B-tree

• Split MBR in the case of overflow
• Line sweeping Compare Cost-X and Cost-Y

Splitting Line
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Splitting Strategy

• 5050 Split
• Instead of 5050 split, other cost measures
• Area,
• Perimeter
• Overlapping Area

1. Make them as COMPACT as possible
2. Preserve spatial proximity as possible
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R-tree An Improvement of R-tree

• Re-Insertion Strategy on Overflow
• Most Popular Index for Multi-Dimensional Index

Overflow