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

elmongui@cs.purdue.edu, mokbel@cs.umn.edu, aref@cs.purdue.edu

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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