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Department of Computer Science
Spatio-Temporal Histograms
Hicham G. Elmongui* Mohamed F. Mokbel+ Walid G. Aref*
*Purdue University, Department of Computer Science+University of Minnesota, Department of Computer Science
SSTD’05 Hicham G. Elmongui
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Motivation
Infrastructure for keeping track and answering continuous queries on moving objects– Moving Queries / Moving Objects– Stationary Queries / Moving Objects– Moving Queries / Stationary Objects– Range Queries, KNN, …
Spatio-TemporalDatabase Server
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Motivation
Spatio-TemporalDatabase Server
How many cars on this freeway? Where is my nearest McDonald’s?
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Motivation
SELECT M.IDFROM MovingObjects MWHERE M.Type = “Truck”INSIDE Area A;We cannot collect statistics statically
(e.g. histograms) and answer queries efficiently over an extended period of
time
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Motivation
Go
to w
ork
Ret
urn
hom
e
Lu
nch
hour
0
0.2
0.4
0.6
0.8
1
12:0
0 A
M
1:0
0 A
M
2:0
0 A
M
3:0
0 A
M
4:0
0 A
M
5:0
0 A
M
6:0
0 A
M
7:0
0 A
M
8:0
0 A
M
9:0
0 A
M
10:0
0 A
M
11:0
0 A
M
12:0
0 P
M
1:0
0 P
M
2:0
0 P
M
3:0
0 P
M
4:0
0 P
M
5:0
0 P
M
6:0
0 P
M
7:0
0 P
M
8:0
0 P
M
9:0
0 P
M
10:0
0 P
M
11:0
0 P
M
12:0
0 A
M
Downtown
A residential area
Not just time makes a
difference, but also space makes
a difference
Nor
mal
ized
Fre
qu
ency
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ST-Histograms
Histograms aware of the underlying
space and time dimensions
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System Architecture
Query Plan
feedbackQuery Executor
Query Optimizer
ST-Histogram Manager
Continuous Query
Dat
a
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Queries as Light Spots
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
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Queries as Light Spots
6.98%
6.98%
6.98%
6.98%
6.25%
6.25%
6.01%
6.01%
6.25%
6.25%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
Q1
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
6.25%
10%
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Queries as Light Spots
6.15%
6.15%
6.15%
6.15%
15.04% 9.84%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
6.01%
5.05%
5.05%
5.05%
6.01%
Q2
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.01%
6.98%
6.98%
6.98%
6.98%
Q1
20%
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15.04% 9.84%15.04% 9.84%
Queries as Light Spots
6.15%
6.15%
6.15%
6.15%
5.05% 5.05%5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
Q1
Q2
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Queries as Light Spots
6.29%
6.29%
6.29%
6.29%
4.22%
15.51%
3.24%
10.15%
5.21%
5.21%
5.21%
5.21%
5.21%
5.21%
5.21%
5.21% 1%
5.05% 5.05%Q2
15.04% 9.84%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
5.05%
6.15%
6.15%
6.15%
6.15%
Q1
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Features of ST-Histograms
No computing capabilities assumed for the moving objects– Moving objects update their location periodically with the spatio-
temporal database server
No patterns assumed for queries– Queries come and go anytime anywhere
Diskless spatio-temporal stream database serverEnable for adaptive query processing
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ST-Histogram Construction/Refining
Initially
Selectivity of a query
Rate of a query to a grid cell
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Experiments – Data Sets
Network-based Generator of Moving Objects (SSDBM’00, GeoInformatica’02)
Map of Greater Lafayette AreaEvery MO updates its location every 10 sec
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Estimation Relative Error vs. Query Size
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.25% 0.50% 0.75% 1% 4%
Query Size
Ave
rag
e R
elat
ive
Err
or
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ST-Histogram’s Stability
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
0 5 10 15 20 25 30 35 40
Time
Av
era
ge
Re
lati
ve
Err
or
0.75%1%4%
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ST-Histogram vs. Random Sampling
0
0.1
0.2
0.3
0.4
0.5
0.6
RS(10%) RS(25%) RS(50%) RS(75%) ST-Histogram
Ave
rag
e R
elat
ive
Err
or
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Related Work
Spatio-temporal histograms– Choi and Chung (SIGMOD’02)– Tao et al (ICDE’03)– Marios et al (SSDBM’03)
Sampling– Random Sampling– Venn Sampling (ICDS’05)
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Conclusion
Aware of the underlying space and time dimensionsImplemented in PLACE (a spatio-temporal database server)Efficient for spatio-temporal streaming applicationsRefined upon feedback from query executorUsed in an online/offline modeAccommodate periodicity in moving objects’ behaviorEnable adaptive query processingAverage relative error 8% for practical query sizes
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The END
Thank You
