Allnearestneighbors Queries in Spatial Databases

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All-nearest-neighbors Queries in Spatial
Databases
SSDBM 2004 June 23, 2004
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All-nearest-neighbors Queries

• All-nearest-neighbors queries Given two
  multidimensional dataset A and B, for each object
  in A, find its nearest neighbor in B
• All-nearest neighbors query application
  Geographic Information Systems (GIS), Data
  Mining, etc.

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R-trees and NN Search

• R-trees Gut84 multi-dimensional index
  structure
• Nearest neighbor (NN) queries
• Depth-first NN query processing RKV95
• Best-first NN query processing HS99
  incremental, optimal I/O cost
• Closest pair queries CMTV00 find the closest
  object pairs from A and B

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All-nearest-neighbors Queries with CP

• All-NN query processing with CP queries HS98,
  CMTV01
• Closest pair query is performed on dataset A and
  B
• A bitmap S0 of size A is used to indicate for
  each point in A, whether its nearest neighbor has
  been found
• If an object pair ltai, bjgt is the first for ai,
  then bj is the NN for ai
• The algorithm terminates when S0ai 1 for all
  ai ? A
• The disadvantage of ANN with CP
• If there is an object ai in A whose NNdist(ai, B)
  is large, all the entry pairs with distance
  smaller than NNdist(ai, B) are required to be
  visited
• Inefficient

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Indexed-based ANN Multiple NN

• All-nearest-neighbors query processing with
  multiple nearest neighbor queries (assume dataset
  B is indexed)
• Perform A NN queries (one for each object in A)
  on R-tree RB
• The order of the NN queries is important if there
  exists an LRU buffer
• If A is not indexed, we sort the objects using a
  space filling curve (e.g., Hilbert) and visit
  them in this order
• If A is indexed, we traverse the R-tree RA
  following the Hilbert order of the entry (with
  respect to the center of the entry MBR)
• Some observations about multiple NN
• The dominant cost is the CPU cost

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Indexed-based ANN Batched NN

• All-nearest-neighbors query processing with
  batched nearest neighbor (BNN) queries
• Retrieves the nearest neighbors for a group of
  objects at a time
• Reduce the number of distance computation
• Apply optimizations like planesweep
• Several criteria for BNN grouping
• The number of points in each group should be
  maximized
• The MBR of each group should be minimized
• Each group should be small enough to fit in memory

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Forming Groups in Batched NN

• Take the objects one by one until any of the
  following constraints is violated
• The number of objects in the group is smaller
  than max_num
• The area of the grouping MBR is smaller than
  max_area

• Determine max_num and max_area
• max_num is determined by the available memory
• max_area is related to the density of the dataset
  B in the area
• Perform a NN search for the first object in the
  group
• Estimate the max_area as the average area of the
  leaf nodes of B visited in the search

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Batched NN

• Take the objects one by one into a group,
  maximizing locality
• If A is not indexed
• Sort the objects in A by their Hilbert value
• If A is indexed
• Start from the root, follow entries recursively
  accordingly to the Hilbert value of their
  centroids
• Find the NN for the objects in the group
• Use NN algorithm (with respect to the MBR of the
  objects)
• Keep the current nearest neighbor for each object
• The algorithm terminates when no better result is
  possible for all the objects

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Non-indexed-based ANN a Hash Approach

• All-nearest-neighbors query processing with
  hashing (assume neither dataset A nor B is
  indexed)

• An observation most of the objects are in the
  same partition as their nearest neighbors

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Hash ANN Query Processing

• Load the corresponding buckets and find the NN in
  the bucket
• For the border objects, put them to a local
  pending set and a global pending list
• When a bucket is loaded, process the objects in
  the pending set
• A 2nd pass might be required to handle buckets
  with non-empty pending set

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Optimization of Hash ANN

• The goal minimize the number of page accesses
  required by the 2nd pass of the algorithm
• Define a good tiling and a good scheduling of
  partitions

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Experiment Settings

• Simulator written in C
• CPU Pentium III 733 MHz
• Page size 4KByte
• LRU Buffer 512KByte
• Dataset United States

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Experiments Indexed Datasets
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Experiments Non-indexed Datasets
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Experiments Self ANN
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Conclusions

• Existing closest pair techniques is not suitable
  for all-nearest-neighbors queries
• Based on whether dataset A and B is indexed, we
  developed different ANN processing methods
• For indexed datasets, batched nearest neighbor
  (BNN) is more efficient than multiple nearest
  neighbor (MNN)
• For large non-indexed datasets, hash-based all
  nearest neighbor (HNN) outperforms BNN build
  the tree on the fly
• Future work (1) extend to high dimensional
  space (2) extend to
  all-k-nearest-neighbors

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• Thank you!
• Questions