Multi-Guarded Safe Zone: An Effective Technique to Monitor - PowerPoint Presentation

Slide1

Multi-Guarded Safe Zone: An Effective Technique to Monitor Moving Circular Range Queries

Presented By: Muhammad Aamir Cheema1Joint work withLjiljana Brankovic2, Xuemin Lin1, Wenjie Zhang1, Wei Wang1

1University of New South Wales, Australia2University of Newcastle, AustraliaSlide2

Introduction

Problem Description: Given a positive value r and a query point q moving in a Euclidean space. Continuously report the objects that lie within distance r of the moving query.Applications:A ship may want to continuously monitor the icebergs within 100 Km of its location.

A person driving a car may want to continuously monitor the gas stations within 10 Km of her location.A fighter plane may want to continuously monitor the enemy targets within its missile range.

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Introduction

Solution Strategy:Assign the query a safe zone such thatresults remain valid if q is in safe zoneRe-compute the results only if q moves outside its safe zoneAdvantages:

Reduced overall computation timeSupports on-demand serviceLow main-memory requirement

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Introduction

Related Work:Distributed processing of range queries (e.g., MobiEyes [Gedik et al. EDBT 04])Continuous monitoring of static range queries on moving objects [Hu et al. SIGMOD 05]

Safe zone based approaches for moving kNN and window queries over static objects [Zhang et al. SIGMOD 03]Contributions:Present a close to optimal technique

Supports object insertions and deletions from the dataset

Rigorous theoretical analysis verified by experiments

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Solution Overview

Internal object: lies within the rangeExternal object: lies outside the rangeSafe zone: (C1 ∩ C2) - C3Guard object: defines the shape of safe zone

AimEfficiently prune objects that do not contribute to safe zoneChecking q lies in safe zone or not

Check distances from guard objects

Data structure

In Disk

R-tree (to index objects)

In memory (temporary)

Location of query

Guard objects (along with associated vertices of safe zone)

Internal objects

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Algorithm Overview

Access entries of R-tree in a suitable orderInitially the safe zone is whole data spaceFor each accessed entry eIf e is not prunedIf e is a leaf or intermediate nodeInsert children of e in the heapIf e is an objectTrim the shape of safe zone using e 6Slide7

Pruning based on rectangles

7qRs

R1maxdist( R1, Rs) < r

R

2

mindist( R

1

, R

s

) > rSlide8

Pruning based on guard objects

A circle that affects the safe zone must pass through the safe zoneSafe zone is contained by intersection of circles of internal objects (e.g., (C1 ∩ C2) - C3 ) The circle must intersect the circles of all internal objects An object cannot affect the safe zone if its distance from any internal object is greater than 2r

Pruning rule: A rectangle R can be pruned, if its minimum distance to any internal guard object is greater than 2r. 8Slide9

Observation

The distance between E and D monotonously increases as D moves from C to F. 9

r

M

E

D’

D

ED =

√

x

2

+ r

2

– 2.r.x. Cos(

θ

) where x = EM

C

F

ED > ED’

θSlide10

Observation

10For every point D on the arc, dist(E,D) < rdist(E,D) < dist(E,A) and dist(E,A) < r

For any arc with end points AB and subtending angle less than 180

o

, the circle of an object E does not affect the arc if its distance to both A and B is at most r.Slide11

Pruning Rule

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Let all arcs of the safe zone have angles less than 180o.An object does not affect the safe zone if its distance to every vertex of the safe zone is at most r.

A rectangle r can be pruned if its maximum distance to each vertex is at most r.Slide12

Observation

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An object E cannot affect the arc AB if it satisfies one of the following; a) E lies within angle range and dist(E,M) > 2r

b) E lies outside the angle range, dist(E,A) > r and dist(E,B) > r

dist(E

2

,D) > dist(E

2

,A) OR dist(E

2

,D) > dist(E

2,B)For every point D on the arc, dist(E,D) > rSlide13

Pruning Rule

13An object E cannot affect the safe zone if it satisfies the observation for each arc of the safe zone.Slide14

Pruned area using all pruning rules

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Access order

15The entries that are closer to the boundary of the range query should be accessed first.Let oi be an object that is closer to the boundary of range query than all current guard objects. The object

oi is guaranteed to affect the safe zone.Slide16

Theoretical Analysis

16Assumptions: A unit space where the objects are uniformly distributed.r: range N: number of objects x: distance the query moves in one time unitEscape probability: The probability that a query leaves the safe zone within one time unit.Slide17

Theoretical Analysis

qdmaxAssumptions: A unit space where the objects are uniformly distributed.

r: range N: number of objects Expected distance: The expected distance a query moves before it leaves the safe zone.Let d

max

be the maximum distance a query can travel before it leaves the safe zone.

For the queries that have

d

max

< C*mup , the expected number of guard objects is 4.14*C.

Experiment results show that 30-50% queries have

d

max < 2*mup, hence for such queries the expected upper bound on number of guard objects is around 8. Slide18

Experiments

Naive: prune every object for which its circle does not intersect the circle of any guard object. Optimal: assume we already know the safe zone, compute traditional range query whenever query leaves the safe zone Real data: 175,813 POIs in North America (data space 5000Km X 5000 Km) Synthetic data: Uniform distribution (used to verify theoretical analysis) 1000 moving queries using

Brinkhoff [1] generator Each query is monitored for 5 minutes[1] T. Brinkhoff. A framework for generating network-based moving objects. GeoInformatica

, 2002

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Efficiency

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Escape Probability

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Expected Distance

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Number of guard objects

22Nominated queries are those for which dmax < 2*mupSlide23

ThanksSlide24

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Trimming Safe Zone

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Let o be the new object and C

i

be its circle

Add o as a guard object

For each circle C

k

of the existing guard objects

compute the intersections of C

i

and C

k

remove the intersection points that lie outside the safe zone

For each existing intersection point p remove p if it lies outside the safe zone Remove objects that do not have any associated intersection point