Querying Mobile Objects in Spatio-Temporal Databases

1
Querying Mobile Objects in Spatio-Temporal
Databases

• Kriengkrai Porkaew1
• Iosif Lazaridis2
• Sharad Mehrotra2
• 1 King Monkuts University of Technology
• at Thonburi, Thailand
• 2 University of California, Irvine
• SSTD 2001, Redondo Beach, CA

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Talk Outline

• Related Work
• Query Types over Mobile Objects
• Indexing Query Evaluation Strategies
• Native Space Indexing (NSI)
• Parametric Space Indexing (PSI)
• Experiments
• Conclusions

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Motivation - VGIS

• VGIS
• a 3D terrain visualization system
• Data
• terrain, weather data, static dynamic 3D
  objects
• Functionality
• spatio-temporal queries over mobile objects

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Update Model

• Linear Motion with constant velocity
• Update consists of ltts, te, xi, vigt
• Next update arrives at time of previous updates
  expiration te.
• Both historical and future queries are supported

location
time
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Related Work

• Spatio-Temporal Index Structures
• Theodoridis et. al. SSDBM 1998 Specifications
  for Efficient Indexing in Spatio-Temporal
  Databases
• Indexing Mobile Objects
• Tayeb et. al. Computer Journal 41(3) A quadtree
  based dynamic attribute indexing method
• Kollios et. al. PODS 1999 On Indexing Mobile
  Objects
• Saltenis et. al. SIGMOD 2000 Indexing the
  Positions of Continuously Moving Objects
• General
• Wolfson et. al. SSDBM 1998 Moving Objects
  Databases Issues and Solutions
• Focus of Current Techniques
• Future Spatio-Temporal Range Queries

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Query TypesSpatial/Temporal Range
location
Q.xH
Q.xL
time
Q.tH
Q.tL
Which objects were in spatial range Q.xL,Q.xiL
during time interval Q.tL,Q.tL?
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Query TypesTemporal kNN
location
Q.xH
Q.xL
time
Q.t
k top objects closest temporally to query time
Q.t that lie in spatial range Q.xL, Q.xH,
ordered by time
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Query TypesSpatial kNN
location
Q.x
1
time
Q.tL
Q.tH
k top objects closest spatial to query location
Q.x during time interval Q.tL, Q.tH, ordered
by proximity
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Indexing ApproachesNative Space Indexing (NSI)

• represents objects with bounding boxes in native
  space (time/location)
• bounding box ltL,Hgt
• L R.tL,R.x1L,,R.xnL HR.tH,R.x1H,,R.xnH

• To eliminate false admission
• line-segment lts,egt
• sO.ts,O.x1s,,O.xns eO.te,O.x1e,,O.xne

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Native Space IndexingRange Query

• Range Query Q
• For a Bounding Box R
• if overlaps (Q, R), i.e., Q overlaps with R along
  the temporal and all spatial dimensions ??
  explore node
• For a line segment L
• if L does not overlap with Q in time ? ignore
• else

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Native Space IndexingRange Query Line Segment
location
TiQ.T? O.T ? Li.T T ?i Ti If T is empty,
ignore Else retrieve
Q.xiH
Q.xiL
time
time
Li.Ttime interval that the line of the object
cuts the upper/lower boundary of the query along
dimension i
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k Nearest Neighbor Algorithm
Priority Queue
answer
h
f
g
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Native Space IndexingTemporal kNN

• Temporal kNN query ltQ.t Q.xiL, Q.xiHgt
• retrieve objects in ltQ.xiL, Q.xiHgt with minimum
  tQ.t-O.t
• explore nodes in ascending order of t using a
  priority queue
• Bounding Box testing
• for each i, if R.xiL, R.xiH not overlap Q.xiL,
  Q.xiH ? ignore
• else, compute t and insert ltt, Rgt in the priority
  queue

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Native Space IndexingTemporal kNN Line Segment
location
Ti O.T ? Li.T Tov ?i Ti
time
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Native Space IndexingSpatial kNN

• Spatial kNN query ltQ.tL, Q.tH Q.xigt
• retrieve the k nearest objects to Q.xi during the
  time interval Q.tL, Q.tH
• explore node in ascending order of d distance
  from Q.xi
• Bounding Box testing
• if R.tL, R.tH not overlap Q.tL, Q.tH ?
  ignore R
• else, compute d mindist (P, Q) ?I di21/2

Bounding Box
Line Segment
xi
diR.xL-Q.xH
di0
Q.xi
di Q.xL-R.xH
time
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Indexing ApproachesParametric Space Indexing
(PSI)

• represent objects with their motion parameters
• time ltts, tegt
• starting location O.xi
• velocity O.vi
• Location Function
• O.xi(t)O.xiO.vi(t - O.ts)
• where ts ? t ? te
• Bounding box R
• lttL,xiL,viL tH,xiH,viHgt

Location (x)
Time (t)
Velocity (v)
Spatio-temporal Query (projected on a bounding
box)

• Historical Queries feasible since past segments
  are kept in index
• Maximum locality since ts the time reference of
  the most recent update is used

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Parametric Space IndexingRange Query

• Bounding Box testing
• if Q.tL,Q.tH not overlap R.tL,R.tH ? ignore
  R
• else compute time interval tov,i that R overlaps
  Q in the native space along dimension i
• Tov,iTi ? Q.T ? R.T
• if Tov,I is not empty on all dimensions, then
  explore R, else ignore it

location
viH
R
viL
time
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Parametric Space IndexingTemporal kNN
Q.t
location

• Bounding Box testing
• compute time interval Tov,i that R overlaps Q in
  the native space along dimension i
• Tov,i Ti ? R.T
• Tov ?i Ti

viH
Bounding Box R
viL
time
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Parametric Space IndexingSpatial kNN
Query
Q.xi
xi
di

• First, compute the temporal overlap
• K.T Q.T ? R.T
• Then, compute Si the extent of R in dimension i
  within the time range K.T
• Compute spriority by taking the mindist of the
  query point Q.xi and the range Si and summing up
  over all dimensions

viH
Si
Bounding Box R
Spriority ?i di21/2
time
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Experiments

• Data
• 5,000 mobile objects moving in a 100x100 grid
• Objects send 1 update/time unit
• Simulations with 1, 2, 4 velocity units were run
• Duration of simulation 100 time units (500,000
  line segments in index)
• Queries
• Ranges of sizes 0.25 to 10 along each spatial
  dim.
• Average results over 1,000-query loads

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Range QueriesI/O Cost
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Range QueriesCPU Cost
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Range QueriesVarying Object Speed
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Temporal kNNI/O Cost
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Spatial kNNI/O Cost
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Interpretation

• Parametric Space Indexing
• compact representation
• no false alarms
• - need transformation
• - not so good locality
• - specific to the type of motion used
• Native Space Indexing
• good locality
• general for all kinds of motions linear,
  circular, constant speed, constant acceleration
• easy to deal with
• - highly overlapped boxes

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Conclusions

• Classification of selection queries over mobile
  objects with range or nearest neighbor predicate
  on space/time
• Query processing techniques using two indexing
  approaches Native and Parametric-Space Indexing
• Native Space Indexing outperforms Parametric
  Space Indexing besides being conceptually simpler