Indexing the imprecise positions of

moving objects

Xiaofeng Ding and Yansheng Lu

Department of Computer ScienceHuazhong University of Science & Technology

Wuhan, China.

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Outline of the Talk

Background

The moving objects with uncertainty

Query evaluation and indexing

Conclusions

Application pull Many applications need to manage imprecise

data Scientific applications Global Positioning System Sensor databases Meteorology system Location based services

The reasons bring imprecision Measurement error Sampling error Update delay Etc..

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Technology push Indexing methods

R-tree, MVR-tree, HR-tree, … TPR-tree, TPR*-tree, Bx-tree, Bdual-trees …

Range search R-tree, MVR-tree, HR-tree,

Nearest neighbor Time parameterized NN Continuous NN Location based NN

Reverse nearest neighbor Stream processing …

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Technology push (Cont.)

Orion DBMS

TRIO project

ConQuer project

U-tree

All the above work assumes that the database has the exact location of each object. But this is rarely possible.

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Technology push (Cont.)

ORION DBMS

* Open-source DB* Open-source DB * Uncertainty * Uncertainty support * DB support * DB enhancementenhancement

Technology push (Cont.)

Uncertain range search [Reynold et al. VLDB 04], [Tao et al. VLDB 05]

Uncertain nearest neighbor search [Reynold et al. SIGMOD 03, TKDE 04]

Uncertain join processing [Reynold et al. CIKM 06]

All existing work considers only uncertain stationary objects.

Uncertain model of moving objects

recorded location in database

uncertainty region

radiusmoving velocity

The moving object’s location is described by a probability density function within the uncertainty region.

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Constrained imprecise range query

Client 2

Client 1

Client 4

Client 3

rq (the area of town center)

Find the clients that are currently in the town center with at least 50% appearance probability.

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Qualification probability

x

U(i,t)uncertainty region R

query region

U(i,t) ∩ R

Client i

Qualification probability:( , )

( , )U i t R

i iP pdf x t dx

Calculation time of an appearance probability in 2D space: 1.3ms

Time for a random I/O access: 10ms

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Goal

Support any pdf

Minimize the number of page accesses

Minimize the number of qualification probability calculations.

Minimize the total cost (I/O + CPU)

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Main idea

For each moving object, pre-compute the velocity constrained region (VCR) to: Instead the uncertainty region

Uncertainty region is usually a polygon VCR is usually a rectangle

Efficiently calculate whether an object appears in a query region with at lest a certain probability

The pdf within VCR is known as Uniform or otherwise

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Quick examples

VCR:

uncertainty region

recorded location in database

moving velocity

velocity constrained region

Dx(t)

Dy(t)

{ 0 0

0 0

Dx(t)= Vx(t ) (t-t )Dy(t)= Vy(t ) (t-t )

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Quick examples (cont.) Suppose the probability density function pdfi(x, t)

of VCRi(t) is a bounded uniform distribution:

( )

( )i

VCRi t RP

VCRi t

{ 1/VCRi(t) if x VCRi(t)0 otherwise

pdfi(x, t) =

If the imprecise range query is evaluated at time t, then the qualification probability will be:

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p-bound

Pre-compute some “auxiliary information” that can be used to efficiently decide whether an object appears in a region

with at least a certain probability without calculating its actual appearance probability.

1 1 2 2{ ( ), ( ), ( ), ( ),...... ( ), ( )}d dL p U p L p U p L p U p

p-bound of a d-dimensional moving object:

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Quick examples The p-bound of an uncertain moving object o takes a parameter

p whose value is between [0, 0.5]: The requirement of Li(p) is that the appearance probability of o on

the left of Li(p) equals p Ui(p) line segments are obtained in the same way.

R

velocity constrained region

Dx(t)

Dy(t)

L1(p) U1(p)

U2(p)

L2(p)

p-bound

Indexing

Indexing is necessary Query time is affected by the number of objects that to

be considered For a large collection of points, it is impractical to

evaluate each point to answer the query.

Indexing the moving object with uncertainty in the virtue of TPR*-tree Velocity constrained index

Other issues Calculation optimization

Nearest neighbor queries

Reverse nearest neighbor queries

Join processing

Metircs for measuring the answer quality

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Conclusions

Notions about uncertain moving objects Uncertain models Kinds of queries.

The effective method for answering constrained imprecise range queries Pre-computed velocity constrained region The concept of p-bound Indexing methods.

Thank you!