Approximate%20querying%20about%20the%20Past,%20the%20Present,%20and%20the%20Future%20in%20Spatio-Temporal%20Databases

1
Approximate querying about the Past, the Present,
and the Futurein Spatio-Temporal Databases

• Jimeng Sun, Dimitris Papadias,
• Yufei Tao, Bin Liu

2
Motivation

• Spatio-temporal databases vs. Data streams
• The monitoring applications
• Traffic supervision
• Mobile users monitoring
• Weather forecasting
• Example
• find the number of vehicles
• in the city center now
• The challenge is to provide fast query response
  in highly intensive environment

3
Problems and methods

• Problems
• How to efficiently store/summarize the
  spatio-temporal information?
• How to approximately answer the query about the
  past, the present, and the future?
• Methods
• Adaptive multi-dimensional histogram (AMH)
• Historical synopsis
• Stochastic prediction method

4
Related work

• Histograms
• Static multi-dimensional histograms
• Equi-depth, Mhist, Minskew, Genhist, SQ
• Query-adaptive multi-dimensional histograms
• STGrid, STHoles, SASH
• Other approximation methods
• DCT, Wavelet, Sketch
• Spatio-temporal databases
• Historical retrieval
• Future prediction

5
Outline

• Introduction
• Problem and proposed methods
• Adaptive multi-dimensional histogram
• Historical synopsis
• Prediction model
• Experiment
• Conclusion

6
Query types
Queries
location
Present Time (PT)
Historical Time (HT)
Future Time (FT)
time
current
past
future
7
System Overview
Historical Synopsis
AMH
Queries
Spatio-temporal updates
PT
Past Index
HT
FT
Prediction Model
8
Histogram

• Partition the space into buckets
• Data within a bucket summarize by the mean
• The properties of a good histogram
• Uniformity within each bucket
• Incremental updateable

bad
good
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Adaptive Multi-dimensional Histogram (AMH)

• Objective minimize WVS?(areaivari) (Minskew
  Acharya, Poosala, Ramaswamy 99)

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Dynamic Maintenance of AMH

• Our scheme record the information during the
  construction and modify the structure as needed.
• 1. information update
• Update the bucket count
• 2. bucket reorganization
• Merge to claim buckets
• Split to reduce WVS

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Information update of AMH
Buckets
n1
n1
b1
b3
b6
b1
n3
n2
n2
mapping
n4
b5
b2
b1
b2
b1
n5
b6
b4
BPT
b5
b4
b3
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Bucket reorganization -Merge

• Merge the subtree that leads to minimal WVS
  increase

BPT
n1
n3
n2
b5
n1
n1
b
b1
b2
n3
n3
n2
n2
Buckets
n4
n4
n4
b5
b5
b1
b
Merge
b1
b2
b1
b2
n5
b6
n5
b6
BPT
b4
b3
b4
b3
b2
Bucket Info 1. region x-, xy-,y 2.
frequency count/area 3. 2nd moment (for
variance calculation)
b5
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Bucket reorganization -Split

• Split the bucket that leads to maximal WVS
  decrease

n1
n1
n3
n2
Split
n3
b5
b
n2
b2
n4
b5
b
b1
b2
b1
b2
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Features of AMH

• Bucket information is updated as new data arrive
• Bucket extents continuously adapt the data
  distribution changes
• The maintenance does not affect the normal query
  processing
• It is interruptible at any moment of time
• It is performed at the CPU idle time

15
Outline

• Introduction
• Problem and proposed methods
• Adaptive multi-dimensional histogram
• Historical synopsis
• Prediction model
• Experiment
• Conclusion

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Historical Synopsis

• AMH maintains the current buckets.
• Past index stores the obsolete buckets.
• Past index
• Packed B-tree
• 3D R-tree

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Prediction Model

• Prediction based on velocity doesnt work!
• It is not realistic to assume velocity remains
  constant between current time and query time
• Velocity is highly dynamic
• We suggest to use only the past and present
  location information to do prediction.

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Prediction Model (cont.)
FT
PT
Parse
Prediction Model
HT
results
forecast the future using any time series
prediction method we use AR
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Outline

• Introduction
• Related work
• Problem and proposed methods
• Adaptive multi-dimensional histogram
• Historical synopsis
• Prediction model
• Experiment
• Conclusion

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Experiment settings

• Datasets
• 2.5M updates for each dataset
• spatial 50K mobile objects from 2 spatial
  dataset
• road from a spatio-temporal generator
  (described in Brinkhoff 2002 )

final
initial
median
Road network
Data distribution
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Robustness with time
Query qlength 6 of the data space 25K
queries uniformly distribute along space and time
spatial
road
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Comparison with conventional histogram

• Minskew (a static spatial histogram) is rebuilt
  every 50k location updates
• tp is the proportion between the cost of AMH and
  that of Minskew
• The re-organization operations of AMH are
  uniformly distributed among the 50k location
  updates.

minskew
spatial
AMH
minskew
road
AMH
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The effect of update intensity
road
spatial
Query type
3D r-tree
b-tree

• B-tree performs better at the high update rate.
• R-tree provides much faster query response.
• In general, when query/update ratio is large
  (gt30), R-tree performs better.

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Conclusion

• We present a comprehensive approach for
  processing queries that refer to any time in
  history.
• The proposed architecture maintains
• an incremental multi-dimensional histogram
• a past index structure for storing the outdated
  buckets.
• Future queries are answered by a stochastic
  method that uses the recent history to predict
  the future.

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QA
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Summary
Historical Synopsis
AMH
0. goal min(WVS) 1. Info update 2.
Reorganization happens when CPU is idle
Prediction Model
Old buckets
Past Index
Forecast based on the present and past.
1.Recent buckets in memory 2.Old buckets dump to
the disk
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Related work

• Static multi-dimensional histograms
• Query-adaptive multi-dimensional histograms
• Other multi-dimensional approximation methods
• Spatio-temporal prediction methods
• Spatio-temporal aggregation methods

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Evaluation over different query types
spatial
road
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Motivation (cont.)

• Spatio-temporal database (STDB) research
• historical retrieval
• future prediction

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Bucket reorganization -Split
n1
n1
n3
n2
n3
b5
b
n2
b2
n4
b5
b
b1
b2
b1
b2
Buckets
Split
Buckets
b1
b
b2
b3
b1
b
b2
b2
b4
b5
b5