Dynamic Queries over Mobile Objects

Iosif Lazaridis1

Kriengkrai Porkaew2

Sharad Mehrotra1

1 University of California, Irvine, USA2 King Mongkut’s University of Technology

at Thonburi, Thailand

EDBT 2002, Prague, Czech Republic

Talk Outline

Problem Motivation: Moving Observers

Preliminaries: Motion Representation and

Indexing

Dynamic Queries : predictive Vs non-predictive

Evaluation Algorithms for Dynamic Queries

Experiments

Conclusions

Problem Motivation: Moving Observers

x

y

x

y

Problem Motivation: Moving Observers

timex

y

observer

query

moving object

Preliminaries: Motion Representation

time

x

tl th

O.x=f(t,)Object O

min(O.x)

max(O.x)

O.x=f(t,’)

Example Representation:

= (x0, v)

O.x = x0 + v(t-tl) tl

x0

slope v

th

Preliminaries: Motion Indexing

time

x

a b c

ab

c

ed gf

d

e

f g

h i j k

h i

jk

Definitions: Snapshot and Dynamic Queries

xQh

time

x

tQ

xQl

Q

Snapshot Query: Q

a

b

time

x

Q0 Q4

Q3

Q2Q1

Dynamic Query: Q0, Q1,…,Q4

c

Query Types: Predictive Dynamic Queries (PDQ)

User trajectory is known beforehand as a sequence of key snapshot queries, K0, K1,…

time

x

K0

K1

K2K3

key snapshot

snapshot

Query Types: Non-Predictive Dynamic Queries (NPDQ)

y

x

P

Q

P Q

Results retrieved in previous query P canbe useful in answering subsequent query Qif

P Q is significant P and Q are temporally close Objects are not too fast-moving

Comparison:Predictive Vs Non-Predictive Queries

Predictive queries are useful when Trajectory is pre-planned (“tour mode”), or stable

Objects are returned in order of appearance along the

known trajectory. Each object is retrieved once.

Non-predictive queries: General case when the next query cannot be inferred

Objects that have been retrieved in the previous query are not

retrieved again if they continue to appear in the next query

An interesting topic of future research: Online adaptation to query behavior

Query Evaluation: Simple Approaches

General “Naïve” Approach Ask each snapshot query separately

Disadvantage: redundant retrieval of objects;

knowledge of trajectory (if any) is not used

Pre-calculate query results for PDQ Evaluate the complete PDQ result set beforehand

Disadvantages

costly pre-computation

observer deviation?

updates?

Query Evaluation: Predictive Queries - Overview

x

timetstart tend

For each tree node, or motion segment (starting from the root) we compute an interval [tappear, tdisappear]

tappear tdisappear

a getNext(tstart, tend) interface returns objects that will appear in view during [tstart, tend] in the order of their appearance time tappear

For a snapshot at time tq, repeated calls to getNext are made until an object with tappear>tq is returned

Returned objects are keyed in order of disappearance time tdisappear and are discarded from the query result as soon as tdisappear tq

Query Evaluation: Predictive Queries - Example

A

C

b

d

E

f

G

h

time

C1 C2

e1 e2

tstart tend

tree node

motion segment

Query Evaluation: Predictive Queries - Motion Updates

g h

Ab c

d e fB

C

0 1

D

2 3 4 5 6 7

E F G H

8 9 10 11

f

3

c

4

head

g h

A

b n c

d fB

C

0 1

D

5 7 2 3 4

F E G H

8 9 10 11

f

n

3

c

head

e mN

4

6 12

M

n

12Before Update

After Update

Priority QueueR-Tree

Query Evaluation: Non-Predictive Queries

y

x

P

Q

SPACE

A

B

Ending time

Starting time

Q

P

C

D

TIME

Experiments: Data and Queries

Data and Index 2-d space of 100x100 space units

Each object updates its motion every ~1 time unit

Objects move with a velocity of ~1 space/time unit

Simulation runs for 100 time units

R-Tree with 4K page size and 0.5 fill factor is used (height=3)

Queries 1,000 trajectories. Snapshot query is issued every 0.1 time units

Varying overlap level between snapshots from 0 to 99.99%

Varying spatial range from 8x8 to 20x20

Experiments: Predictive Queries I/O

Experiments: Predictive Queries CPU

Experiments: Non-Predictive Queries I/O

Experiments: Non-Predictive Queries CPU

Conclusions

A Dynamic Query is a sequence of queries

generated by a mobile observer

We proposed algorithms to evaluate Dynamic

Queries for both the general (Non-Predictive) and a

special (Predictive) case

Future work: Generalizing Dynamic Queries

Adapting query processing to the behavior of the mobile

observer