ST2Btree: A SelfTunable SpatioTemporal B tree Index for Moving Objects

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ST2B-tree A Self-Tunable Spatio-Temporal B-tree
Index for Moving Objects
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Outline

• Introduction
• Related work
• The ST2B-tree
• The structure
• Self-tuning framework
• Experiments
• Conclusion

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Introduction

• Basic characteristics of moving objects
• Large number of objects
• Frequent location updates
• Fast query processing
• The way out effective and efficient indexes
• Another aspect of moving objects
• Highly dynamic
• Overlooked by existing indexes

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Motivation

• Data diversity
• Space
• Time
• Space-time

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• Time 05/06/2008 0503 pm

The number of objects varies in different regions
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Motivation

• Data diversity
• Space
• Time
• Space-time

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• Time 05/06/2008 0805 am

• Time 05/06/2008 0503 pm

The number of objects changes with time.
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Motivation

• Data diversity
• Space
• Time
• Space-time

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• Time 05/06/2008 0805 am

• Time 05/06/2008 0503 pm

The distribution of objects also changes with time
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Motivation

• Data diversity
• Space
• Time
• Space-time

Our aim to develop index that is adjustable to
these data diversities.
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Outline

• Introduction
• Related work
• The ST2B-tree
• The structure
• Self-tuning framework
• Experiments
• Conclusion

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Moving Objects Indexes

• Data Partitioning
• TPR-tree SIGMOD'00, TPR-tree VLDB'03
• Space Partitioning
• Bx-tree VLDB'04, Bdual-tree VLDBJ'08
• SINA SIGMOD'04, CPM SIGMOD'05
• STRIPES SIGMOD'04

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Quick review on the Bx-tree

• Bx-tree B-tree Space Filling Curve (SPC)
• SFC 2d location ?1d value
• 2d range query ? Several 1d range queries

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Pitfall of fixed space partitioning

• Coarse Partitioning
• Too many objects in a cell, indistinguishable to
  the index

For updates - Overflow pages
For queries - More false positives
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Pitfall of fixed space partitioning

• Fine Partitioning
• Few objects in a cell

For queries - Fewer false positives, but - Need
to search more cells
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The ST2B-tree

• Find a way to dynamically partition the space in
  order to make the index adaptable to the data
  diversity.

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Outline

• Introduction
• Related work
• The ST2B-tree
• The structure
• Self-tuning framework
• Experiments
• Conclusion

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The ST2B-tree Index in the space

• Mapping 2d location into 1d value KEYspace
• Given a set of n reference points RP0 , RP1 , ,
  RPn-1
• The space is partitioned into n disjoint regions
  (Voronoi Diagram)
• Each RPi has a grid Gi that covers its Voronoi
  cell
• An object is indexed in the grid of its nearest
  RP

KEYspace i ? cid(p , Gi)
RP3
RP0
RP4
RP2
RP1
RP5
RP6
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The ST2B-tree Index with the time

• The time is divided into segments, T in length (T
  is the maximum update interval)
• Each time segment has a fixed Tref.
• An object is indexed with its location at
  reference time Tref.
• The B-tree is partitioned into two halves. Each
  half corresponds to a time segment.
• Time rolls over the two halves.

BT1
BT0
BT0
BT1
4T
T
2T
3T
0
tnow
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The ST2B-tree Spatio-temporal
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Deal with the diversity

• Partition the space with a set of reference
  points ? Data skew in space
• Each RP partitions the space with different
  granularity for each half ? Change of data
  cardinality with time.
• Use different set of reference points for the two
  halves ? Change of data distribution with time

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Outline

• Introduction
• Related work
• The ST2B-tree
• The structure
• Self-tuning framework
• Experiments
• Conclusion

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The ST2B-tree Self-Tuning

• Tuning framework

Updates
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• Histogram
• 2d grid, collecting statistics about objects in
  each cell
• the number of objects
• the centre of objects in a cell.

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How the tuning works?

• At each transition time iT
• The Timer triggers the online tuning process
• Online Tuning module computes
• the new set of reference points
• grid granularity of each reference point
• Updates information in the Reference Table
• Reset the statistics in the Histogram

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• Online Tuning
• Select new reference points based on the
  statistics
• Region growing
• Density-based clustering, e.g. DBSCANKDD96,
  OPTICSSIGMOD99
• Empirically, based on seasonal patterns
• Determine the optimal granularity of each
  partition
• Based on the object density in the Voronoi cell
  (see our paper for details)

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BT0
BT0
BT1
tnow
3T
0
2T
T
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Outline

• Introduction
• Related work
• The ST2B-tree
• The structure
• Self-tuning framework
• Experiments
• Conclusion

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Performance Study

• Datasets
• Randomly selected hotspots
• Gaussian distribution around each hotspot
• Comparative study
• The Bx-tree is optimized in the beginning
• The benefit of self-tuning

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Time Diversity

• Increasing Data Cardinality

The benefit increases with increasing number of
objects.
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Space-Time Diversity

• Increasing data skew

The benefit increases with increasing degree of
data skew.
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Conclusion

• ST2B-tree Self-Tunable Spatio-Temporal B-tree
• Select the way of space partitioning based on
  data distribution
• Determine the granularity of space partitioning
  based on data density
• Discriminate between regions of different
  densities
• Adapt to changes in workload with time

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• Thank You !

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The effect of grid granularity
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Basic Query Algorithm

• Range Query
• Search both halves of the tree
• Enlarge the query region to the corresponding
  Tref
• If the Voronoi Cell a RP intersect the enlarged
  query region
• Compute the intersection
• Transform the intersected region into 1d range
  queries
• Search the B-tree with each of the 1d range
  queries
• Refinement on the records returned
• kNN Query
• Perform as incremental range queries
• Enlarge the query region until k nearest
  neighbors are found

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Query Enlargement
BT0
BT1
iT
(i1)T
(i2)T
Tref0
R0
tq
Tref1
R1
R
We want to find out all objects that inside R at
tq. It is possible that some object in R0 at
Tref0 or R1 at Tref1 then move into R at tq.
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Spatial Diversity
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Time Diversity

• Decreasing data cardinality

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Data Distribution
Time Round 0 Time Round 5 Time
Round 9
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Concurrent Operations