Querying Mobile Objects in Spatio-Temporal Databases
Kriengkrai Porkaew1
Iosif Lazaridis2
Sharad Mehrotra2
1 King Monkut’s University of Technology at Thonburi, Thailand
2 University of California, Irvine
SSTD 2001, Redondo Beach, CA
Talk Outline
Related WorkQuery Types over Mobile ObjectsIndexing & Query Evaluation Strategies
Native Space Indexing (NSI) Parametric Space Indexing (PSI)
ExperimentsConclusions
Motivation - VGIS
VGIS a 3D terrain visualization system
Data terrain, weather data, static & dynamic 3D
objects Functionality
spatio-temporal queries over mobile objects
Update Model
Linear Motion with constant velocityUpdate consists of <ts, te, xi, vi>
Next update arrives at time of previous update’s expiration te. Both historical and future queries are supported
time
location
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
Query TypesSpatial/Temporal Range
Which objects were in spatial range [Q.xL,Q.xiL] during time interval [Q.tL,Q.tL]?
time
location
Q.tL Q.tH
Q.xL
Q.xH
Query TypesTemporal kNN
k top objects closest temporally to query time Q.t that lie in spatial range [Q.xL, Q.xH], ordered by time
time
location
Q.t
1
2 3
Q.xL
Q.xH
Query TypesSpatial kNN
time
location
Q.tL
1
3
Q.tH
4
Q.x2
k top objects closest spatial to query location Q.x during time interval [Q.tL, Q.tH], ordered by proximity
Indexing ApproachesNative Space Indexing (NSI)
represents objects with bounding boxes in native space (time/location) bounding box: <L,H> L =R.tL,R.x1L,…,R.xnL ;
H=R.tH,R.x1H,…,R.xnH
L
s
e
HX
Time
Object’s trajectory
Y
To eliminate false admission: line-segment: <s,e> s=O.ts,O.x1s,…,O.xns ;
e=O.te,O.x1e,…,O.xne
Range Query QFor 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 …
Native Space IndexingRange Query
Native Space IndexingRange Query – Line Segment
time
Q.xiH
Ti
time
O.T
Q.T
Li.T=time interval that the line of the object cuts the upper/lower boundary of the query along dimension i
Li.T
Q.xiL
locationTi=Q.T O.T Li.T
T = i Ti
— If T is empty, ignore
— Else retrieve
k Nearest Neighbor Algorithm
A
B
AB
Priority Queue
A
CDE
C
D
EBCDE
B
fghf
g
h
fCDEgh
f answer
Native Space IndexingTemporal kNN
Temporal kNN query: <Q.t; Q.xiL, Q.xiH>
retrieve objects in <Q.xiL, Q.xiH> with minimum t=|Q.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 <t, R> in the priority
queue
otherwise0
t.Rt.Qift.Qt.R
t.Rt.Qift.Rt.Q
t LL
HH
Native Space IndexingTemporal kNN – Line Segment
time
location
O.T
Li.T
Ti
Q.t
otherwise0
TQ.tifTQ.t
Q.tTifQ.tT
t Hov,Hov,
Lov,Lov,
Ti= O.T Li.T
Tov = i Ti
Spatial kNN query: <Q.tL, Q.tH; Q.xi>
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 di2]1/2
Native Space IndexingSpatial kNN
xi
Q.xi
di=R.xL-Q.xH
di= Q.xL-R.xH
di=0
time
Q
Q
Q
Bounding Box Line Segment
Indexing ApproachesParametric Space Indexing (PSI) represent objects with their
motion parameters time <ts, te>
starting location O.xi
velocity O.vi
Location FunctionO.xi(t)=O.xi+O.vi(t - O.ts)
where ts t te
Bounding box R=
<tL,xiL,viL; tH,xiH,viH>Velocity (v)
Time (t)
Location (x)Object’s motion
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
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,i=Ti Q.T R.T
if Tov,I is not empty on all dimensions, then explore R, else ignore it
time
viH
location
Ti
Parametric Space IndexingRange Query
Q.T
viL
R.T
R
Tov,
i
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
viL
time
Bounding Box R
tpriority
Parametric Space IndexingTemporal kNN
Q.t
Ti
R.T
location
Tov,i
otherwise0
TQ.tifQ.tT
TQ.tifTQ.t
t Lov,Lov,
Hov,Hov,
priority
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
Parametric Space IndexingSpatial kNN
viH
time
xi
Bounding Box R
Query
Si
di
Q.xi
viLviL
R.T
Q.T
K.T
Spriority = [i di2]1/2
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
Range QueriesI/O Cost
Range QueriesCPU Cost
Range QueriesVarying Object Speed
Temporal kNNI/O Cost
Spatial kNNI/O Cost
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
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
Recommended
