On The Use Data Reduction Algorithms for Real-Time Wireless Sensor Networks

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On The Use Data Reduction

Algorithms for Real-Time Wireless Sensor Networks

Andre L.L. de Aquino1, Carlos M.S.

Figueiredo1 2, Eduardo F. Nakamura1 2,

Antonio A.F.

Loureiro1,

Ant6nio

Otaivio

Fernandes1, Claudionor J.N. Coelho Jr.1

1

_{Department of Computer Science,}

_{Federal University of Minas Gerais, Belo Horizonte, MG, Brazil}

Email:

{alla,mauricio, nakamura, loureiro, otavio}@dcc.ufmg.br

2

_FUCAPI

_-

_{Research and}

_{Technological Innovation Center, Manaus, AM, Brazil}

Abstract

This work presents the design of real-time applications

for wireless sensor networks (WSNs)by usinganalgorithm

based on data stream to process the sensor data. The

pro-posed algorithm is based on sampling techniques applied

to datahistograms created from original data streams

ac-quired by sensor nodes. As a result, the algorithmprovides asample oflognitemstorepresent theoriginal data stream

of n elements. In this work, we show how to use the data

reduction algorithm in real-time WSN design.

1. Introduction

Despite thepotential of their applications, wireless sen-sornetworks (WSNs)[1]haveseveralresourcerestrictions,

suchas low computationalpower, reducedbandwidth, and

limitedenergy source. For these networks, there are two

main types ofapplications: monitoring and actuating

ap-plications [6,7]. Manyof theseapplications have real-time deadline requirements, for example, military, surveillance

system, biometric sensors, and intrusion detection [3, 8].

Real-time solutions for WSNs are often based on existing

protocols, for example, network and link layers[3,5]. There

areworks which addressdesign solutions suchas

architec-tures or models to apply real-time in WSN [8]. None of

these proposals consider application aspects such as data

quality orapplicationrequirements. Inthiswork,weshow

real-time application design for algorithms that consider

dataquality aspects.

In some applications for WSNs, datausually arrives in anonline fashion, isunlimited, and there isnoorderinthe

arrival of data to be processed. Data with these features

arecalled datastreams [10]. Due tothe constraints of sen-sornetworks, sendingalargeamountof datacantake alot

of time. As aconsequence, ahigh delay willprobablynot

meetreal-time requirements ofagivenapplication.

There-fore,we mustprovide techniquesto control theamountof

datathrough the network and itsconsequentdelay.Inorder

todothis, manydatastreamtechniques thatcanbe usedin

WSNs. Inthiswork, we use asampling data stream

tech-niquetoreduce the data traffic.

General research in data stream algorithms tries to

es-tablish lower bounds for datastream algorithm classes or

presentspecificapplications thataremodeled by using data

stream algorithms [2, 10]. In WSNs, the network can be

consideredas adistributed database where some functions

(e.g. maximum, minimum, and average) are computed

in-network or they use the resources available at a

sen-sor database and apply them to extract management

in-formation from the WSN, such as energy and location of

nodes [4, 9]. Current sensor databases are notsuitable for

WSNs, since nodes have too few resources and real-time

aspects are notconsidered.

Inthiswork,weshowareal-timeapplication design for

WSNs when data reduction algorithms are applied. The

algorithm reduction presented is based in sampling tech-niques. Weevaluate thedelay metric for data delivery ver-sustheimpact of thesamplesizeonthe dataquality. Simu-lation results reveal that by using the designguidelines the

real-time deadlines are met and the networkrequirements

canbe reduced while keeping limited dataquality.

More-over, results show the efficiency of the proposed reduc-tionalgorithmby extending the network lifetime and

reduc-ing the delay without losingdata representativeness. The

proposed algorithm can be very useful to design

energy-efficient and time-constrainedsensornetworks.

This work isorganizedasfollows.InSection2,weshow howtodesign real-timesensornetworkapplications by

us-ing datastreamsalgorithms. Next,inSection

3,

wepresent

the data reduction algorithmfor summarizing sensor

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2. Design of Real-Time WSN

Applications

This section discussesreal-time applicationdesign based

on data reduction algorithms, in our case, a data stream

basedalgorithm. InFigure 1,we presentthe desired

behav-ior of the data stream considering real-time requirements.

Oncea sensornode receivesadatastreamfrom thewireless

medium the data stream is classified by the Stream orga-nizer, and theStream processingchooses thesample sizeor

particular algorithm for generating the sample. The blocks

aredetailedasfollows:

applications usually use probabilistic methods to treat the

data and haveno communication acknowledgment. These

aspectshide theuseof hardreal-time. Inthedesign ofasoft

real-time system, we mustknow the delaybehavior of the

data for eachsolution being used. In our case,thedeadline

requirements of the applications canbe met by the stream

algorithmsortheadoptedsample size; and (iii)Data

reduc-tiondecision: inthelast stepof thedesign, the decision of the bestsolution to treat the stream input depends on the network requirements,deadlines, and data quality. This de-cisioncanbeon-lineorindesign level. The dataquality is important because the reductionmaydegrades the data.

3. Data Reduction

Algorithm

The data reductionproblemtoattend the design of Sec-tion2,canbe statedasfollows:

Figure 1. Real-time stream application.

The first design phase is the organization of the streams

generatedinthesensornetwork,Stream organizer. Thiscan

be doneaccordingtothefollowing classification: Sensing is themostnaturalstream. It representsthe sensed datainthe

network and its transmissionmodel dependsonthe network

communication type. In this case, we generally maintain

the data values. Infrastructure is usedto supportnetwork

functions such as routing, data fusion, and data

compres-sionalgorithms. Forexample, the data being forwardedin

theroutingprocess canbe consideredas adata streamand beprocessed by adata stream algorithm. In thiscase, the

use oforiginal data depends on the application. For each

stream type we have a different treatment and deadlines.

In a real-time application design, the Stream organizer is responsible for identifying the data streamusing the infor-mation of received data. This fact allows thestream tobe properly processedtoattendreal-time requirements.

In the seconddesign phase, Stream processing, agiven

stream executesthree streamprocessing functions: (i)

Net-work requirements: there are different sensor network

re-quirements(scalability,energy,packetloss,delay, and

qual-ity of data). These requirementsareusedtodecide the best

reduction solution tobe used in the network. This occurs

because the reduction may lead to different outputs with

different "data qualities"; (ii) Real-time deadlines: to use

deadlines in a sensor network, we mustconsider hard and

softreal-time applications: Hardreal-timeapplications are

typicallyfound wheninteractingat alow level witha

phys-ical hardware, inembedded systems. Softreal-time

appli-cationsaretypicallyfound when there is aneedtoperform

some concurrent access to adatastoragefrom different pro-cesses. In sensornetworks, it is common the use of soft

real-time because the environment is notcontrolled. The

Problem Statement: Given a sensorstream, we

want to meet WSN requirements by reducing

data traffic (by using techniques based on data

streams) and assuring a minimum data quality

thatallowstoreduceenergyconsumption and

de-lay.

Thisproblem canbe further assessedby answering the

following questions: (i) Time limits: What are the time limits for real-time datastream applications in sensor

net-works? In real-time design, we must determine the time

limits ofour solutions. In general, alower bound can be

determinedby the shortest path between source and sink

nodesconsideringonlyonedatastreamofagiven size. One

stream canbe usedtopreventtheinfluence of other network characteristics suchasrouting stack saturation; (ii)Data

re-duction and dataquality: How can weevaluate thequality

of theprocessed data? Due tonetworklimitations and data characteristicsonly samplesof the datastream canbesent.

Thus,we mustevaluateifthe reduced data isrepresentative.

Toperform this evaluationwe can usestatistictests toknow whether theoriginalsensor streamand thesampledone are

equivalent, andalso comparethe distance between the av-erage of their data values; and (iii) Project requirements: Can the desired behavior of data streamapplications,

con-sidering real-time requirements presented in Section 2, be

achieved? To make it possible we need to know the

be-havior of theproposed solution regarding all requirements

addressedin Streamprocessing. FortheStream organizer,

weonly identifythepackettype. Inthiswork,weattend the

Streamprocessingrequirements by usingouralgorithm.

Thesampling based data streamalgorithm is motivated

by the problem stated above. The data reduction will be

achieveby sampling the original data. This solution aims

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Algorithm 1: Pseudo-code of thesampling algorithm. Data: stream[n]-window of original data stream

Result: sample[m]-sample set resulted

1 begin

2 Sort(stream)

3 widthClass<-"Histogram class width"

4 first <- stream[O]

5 numElemColStream O- 0

6 indexO-0

7 j -O

8 fori -0ton -do

9 if stream[i] > f irst + widthClass or i n 1 then

10 numElemColSample

<-[m X numEl emColStreaTm 11 whilenumElemColSample > 0 do

12 index <-"Random elementinthehistogramclass"

13 numElemColSample

numElemColSample -1

14 sample[] [- jstream[index]

15 -iJ+1

16 end

17 numElemColStream O- 0

18 first -- stream[i]

19 end

20 numElemColStream<-numElemColStream +1

21 22 23 end

end

Re- -sort( sample) {accordingto theoriginalorder};

Our sampling-based algorithm provides a solution that

al-lows the balance between best data quality and network

re-quirements. The sample size canvary, but itmustbe

rep-resentative to attend the data similarity requirement.

Ac-cordingtonetworkrequirements, we can settheamountof

samples betweenlognandn. Thus, itcanattend thequality requirementsinrelationtothe networkrequirements.

The sampling algorithmcanbe divided into the

follow-ing steps: (i) Build a histogram of thesensor stream; (ii)

Create a sample based on the histogram obtained before.

To createsuchasample, werandomly choose the elements of eachhistogramclass, respecting the sample size and the class frequencies of the histogram. Thus, theresulting

sam-ple will be represented by thesamehistogram; and (iii) Sort the data sample accordingtoits order intheoriginal data.

Thepseudo-code of thesampling algorithm is givenin

Al-gorithm 1.Wealso considern asthe number ofelementsin

theoriginal datastream,andm astheadoptedsample size.

Analyzing the Algorithm 1 wehave: Line2 executes in

(n

log

n).

Lines 11-16 define the inner loop that

deter-mines the number of elements at each histogram class of

the resulting sample, which takes

0(m)

steps. Lines

8-21 define the outer loop in which the input data is read

and the sample elements are chosen. Because the inner

loop is executed only when condition in line 9 is

satis-fied, the overall complexity of the outer loop is

0(n)

+

0(m)

=

O(n

+

m)

since wehave an interleaved

execu-tion. ConsidernumClass the number of histogram

classes,

numElemColStreami

and numElemColSamplIe,

re-spectively,thecolumnsinoriginalandsampledhistograms, where0 < i < numClass. Basically, beforeevaluating

the condition ofline6,

nTumElemColStreami

is counted

and ntm-lass interactions are executed. Whenever this

condition is satisfied,

numElemColSamplei

isbuilt and

m _{interactions are executed}_{(loop 11-16).} _In_order numClass

tobuild thecomplete histogram, we must coverall classes

(nTumClass), then we have nTumClass x ( nl+m±7) =

n+ m.Line22 re-sortsthesampleinO(m log m). Thus, the overallcomplexity is 0(nlogn)+0(n+m)+

O(mlog m) = O(n log n), sincem < n. Thespace

com-plexity isO(n +m) = O(n) becausewe storetheoriginal

data stream and the resulting sample. Since every source

nodesends itssamplestreamtowards the sink, the

commu-nicationcomplexity isO(mD),where D is thelargestroute (inhops)inthe network.

4. Algorithm Evaluation in Real-Time Design

Fromthe design phases showedinSection2 inorderto

analyze the data reduction behavior in real-time

environ-ment, weconsider fouraspects: (i)Stream organizer: We useonlyonetype of datastreamarriving sensing; (ii)

Sen-sornetworkrequirements: Weanalyze theenergybehavior

using our solution because energy is the most import

as-pectofWSNs; (iii) Real-time deadlines: Weanalyze the de-lay limits forourdata reductionsolution and observe which

deadlines canbe supported by our solution; and (iv)Data

reduction decision: We analyze the data quality behavior

foroursolution and discuss about the project decision from theresults combination.

Theevaluation of thealgorithms is basedonthe follow-ingassumptions: (i) Simulation: Weperformourevaluation

through simulations andusethe NS-2 (Network Simulator

2) version 2.30. Each simulated scenariowasexecuted with

33 random topologies. At the end, for each scenario we

plot theaveragevalue with95% of confidence interval; (ii)

Network topology: We use a tree-basedrouting algorithm

calledEF-Tree [11] as theroutingprotocol, thedensity is keptconstant, and all nodes have the samehardware

con-figuration. Toanalyze onlytheapplication, thetreeisbuilt just once,before the traffic starts; (iii) Streamgeneration: The streams usedby the nodes are always the same, fol-lowinganormal distribution, where the valuesarebetween

[0.0;

_1.0],

and the generation periodicity is 60s. The size

of the data packet is 20 bytes. For larger samples, these

packets arefragmented bythesources andre-assembledat

the reception; and (iv) Evaluatedparameters and stream

size:Wevaried the number ofnodes, streamsize, and

num-ber of nodesgenerating data. Foreachevaluatedparameter we analyzed the application and network behaviorby

us-ingsamplesizesofn _and_log_n. _All_parameters_used_in_the simulationsarepresentedinTable 1.

Inorderto evaluate the dataquality by distribution

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Table 1. Simulation parameters.

Parameter Values Parameter Values

Network size Varied with density Simulation time 5000s Queue size Varied with stream Traffic start I000s

Sourcelocation Random Trafficend 4000s

Number of sources 1, 5, 10, 20 Streamperiodicity 60s Number of nodes 128,256, 512, 1024 Sinklocation 0, 0 Stream size (n) 256, 512, 1024, 2048 Radio range (m) 50 Sample size log n,n/2,n Bandwidth(kbps) 250

usetheKolmogorov-Smirnovtest(K-S test) [12]. Thistest

evaluates if two samples have similar distributions, and it

is not restricted tosamples followinganormal distribution. Moreover, asthe K-Stest only identifies ifthesample dis-tributions aresimilar, it is also importanttoevaluate the

dis-crepancyof the valuesinthe sampledstreams, i.e., ifthey stillrepresenttheoriginal stream. Toquantify this

discrep-ancy (Data Error) we compute the absolute value of the

largest distance between theaverageof theoriginal data and thelowerorhigher confidence interval values(95%) of the

sampled data average, Data Error = Max{ luwervalue

Generateavgl

_highervale-

Generateavg }, where the pair

(lowervalue;

highervalue)

is the confidence interval of data sample and Generateavg is theaverageoforiginal data.

In thefollowing, weshow the simulation results of the

datareductionalgorithmtoaddress thedesign requirements forreal-time applications.

DEADLINE BEHAVIOR. An important issue to be

considered when evaluating real-time requirements is the

possible time limits of each sample size of data streams.

These time limitscanbevery difficult todetermine dueto

the possible dynamic conditions during the network

oper-ation, such as different number ofsources, data sizes, and

topologies. Thus, weperformed this study by considering

theamountof data sent inthe network andby changing the

samplesizes.

In order to do this,

weconsiderannetwork

with a fixed size of 256 Table 2. Time limits

nodes, running thetree- stre n n log n

based routing infras- 256 0.62 0.36 0.11

512 1.12 0.67 0.11

tructure, and only one 1024 1.98 1.19 0.11 source of data generat- 2048 3.70 1.94 0.11

ing streamswith

differ-entsizes. We usethelowestaveragedelayobtainedthrough

simulations by considering random topologies and a tree

with the minimum number ofhops between the nodes. The

delayis determinedby measuring the time between the first datapacketsentby the source and thelast packet received by the sink, i.e., it is the time for a stream to be entirely

receivedby the sink. Table 2summarizes the time

limits,

in seconds, for our data reduction algorithm using

differ-entsamplestrategies and the considered data stream sizes.

These limits are used in the Real-Time Deadline module

present in Section 2 to help innetwork decision when our

solution is applied in a real-time environment. So, ifthe deadline requirementmetthis time limits our solutioncan

be usedinthereal-timeapplication.

A moredetailed evaluationof thedelayperformance is presented in Figure 2. This evaluation considers the delay of the entire networkto delivery adatapackettothe sink.

Inthisevaluation, we usedifferentsample sizes (lognand

) and the complete sensor stream (n). These cases are

analyzed with different network scenarios by varying the

networksize, the amount of generated data at the source,

and the number ofsources.

We observeinallcasesthat when the sample size is

di-minishedthedelay diminishes accordingly. Thelogn

sam-ple is the best result because the number of elements in

packet has a little increased. Analyzing the figures

sepa-rately, whenthe number of nodes varies (Figure 2(a)), the delay variesalittle. Thisoccursbecauseonlyone sourceis used, and both the size of thesensor streamand the network density didnotchange. Inthis scenario, the logn sample

hasless impactonthedelay.

When the size of the sensor streamvaries (Figure 2(b)),

we canobserve theimpact ofoursolutionsinthedelay. The lognsample has the best performanceinallcases,and the delay doesnot varywhenthesample size increases. In the

lognsample, thisoccursbecause the number ofelementsin

packet is increasedonlywhenweincrease thesensor stream

size (256, 512, 1024, 2048). The other results (samples of

2 and

n)

haveworse

performances

because the number of packets is increasedproportionallywhen thesensor

stream-ingsize is increased.

When the number of nodesgenerating data varies

(Fig-ure2(c)), thesampleoflognhave the bestperformance for allcases. Thisoccursbecause, inthisscenario,more

pack-ets arepassing through the network when we increase the

number of nodes generating data. Each source using the

sampleoflogn usesonly onepacket (the packet size isno

more than 20bytes) to send its data to the sink. For the

otherresults (samplesofn' and

n)

eachsourcenode gener-ates morethan oneapplicationpacket,overloadingthe

net-work, andcausing delay. These results are close to time

limits showedinTable 2.

ENERGY BEHAVIOR. This evaluation considers the

energyconsumption of the entire networktodeliveryadata

packet to the sink. Again, we use different sample sizes

(logn and n) and the complete sensor stream (n). These

cases areanalyzedwith different network scenariosby

vary-ing the networksize, the amount ofgenerated data at the

source, and the number ofsources. Accordingtothedelay

behavior, as a result when the sample size

decreases,

the

consumedenergydecreases for the same reasonthatdelay

behavior. Again,thesameeffect of the number of node

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Packet delay

7 _* _{log n}

0 - * n/2

o n

-5

128 256 512 1024

Number ofnodes

(a) Different networksizes.

Packet delay

7 _* _{log n}

* n/2

On

256 512 1024 2048

Amount of data generated at the source node

(b) Different stream sizes.

Packet delay

7r logn

s 5 n/2

Onn

1 5 10 20

Numberof nodesgenarating data

(c) Differentnumberof sources.

Figure2.Average delay.

of nodes generating data (Figure 3)vary we canobserve the

impactontheenergy whenour solution is used. In the all

cases,thesample lognhas the best performance. These

re-sults are usedin theSensorNetworkRequirementmodule

presentin Section 2tohelp deciding when the application needstosaveenergy.

Energyconsumption

errorisconstant, since the data lost is small. The greatest error occurswhenwe use asmallersample size but the data

similarity is kept.

Vertical distance inKS-test

10 20

Number ofnodesgenaratingdata

1 10 20

Number of nodesgenaratingdata

Figure 3. Total energyconsumption.

DATA QUALITY BEHAVIOR. Here, we presentthe impact ofour solutionby evaluating the data quality. The

sampling solution looses information inits process,

there-fore it isimportanttoevaluateitsimpactonthe dataquality.

Again, the impact of the sampling solution is made through the K-S testand theaverage error. Like the network

eval-uation, we usedifferent samplesizes(lognand )and the

completesensor stream(n) indifferent network scenarios. We varythe network size, theamountof data generated at

thesource,and the numberofsources. Here,weshowonly

the number of sources result because in all scenarios we

have thesamebehavior.

Figure 4 shows the similarity between the original and sampledstreamdistributions. The difference between them is called ks-diff. The results show that when the sample size is decreased theks-diff increases. Because the datastreams

are generated between [0.0; 1.0], ks-diff is 20% for logn

sample sizes, and ks-diffis 10% for n sample sizes. The

Figure4. K-S distance.

We also evaluate the data quality through the

discrep-ancybetween the original and sampledstreamaverage

val-ues (Figure 5). This error we call data-error. Like the

ks-diff, when thesample size decreases, the data-error

in-creases. However, data-error is 10% for samplesoflogn,

and data-error is almostzeroforsamplesof . Again, the

erroris constant for the same reason of the ks-diff. How-ever animportant observation is that the data-error is the

samefor

samples

of andn.

Therefore,

ifwewant to

_keep

the maximum dataquality, considering thedata-error, we cansendonly samples of n. These results areused in the

DataReductionDecisionmodulepresentedinSection 2 for

help in decision about the data quality when the application

requirequalityindataprocessing.

Insummary, whenwe analyze the combination of data

quality, network behaviorand deadlines in the Data Reduc-tion Decisionmodule, presentedinSection2, weconclude

that: (i) the sample oflogn reduces the energy

consump-tion anddelayby reducingtheamountof databeing

trans-mitted.However, the data quality is affectedinthe distribu-tionsimilarity (20%) andaveragediscrepancy (10%). But

* logn * _n/2

O n

rS'.

X .

_.~

* _logn * _n/2

o n +

E + +4

~~~~I t

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Dataerror

1 10 20

Number of nodesgenaratingdata

Figure 5. Averageerror.

thisquality maybeacceptable in WSNs applications when

the network restrictions are strong; (ii) the sample of n is interesting when the application priority is theaverage

dis-crepancy (near zero); and (iii) it is interesting not to use ouralgorithm (sample of n) whenwehavetokeep thesame

dataquality similarity andwedonothavetoworryabout the

WSN restrictions. The resultsanswerthequestions Data

re-duction and dataqualityandcanbeappliedtotheproblem

addressed in Section 3.

5.

Conclusion

In real-time wireless sensor networks applications, a

veryimportant requirement is the timetodeliver such data

streams to the sink, and, as discussed in this work, the

amount of data in transit through these constrained

net-works hasagreatimpactonthedelay. Thus, weproposed

and evaluatedabased datastreamalgorithm thatuses a

sam-pling over ahistogram techniquetoreduce datatraffic, and consequently the delay andenergyconsumption. This work

representsawaytodeal withenergyand time constraintsat

theapplication level,as acomplementary viewtosolutions thattreatthisprobleminlower network levels.

The results show theefficiency of the proposed method by extending the network lifetime since data transmis-sion demands lots ofenergy andreducing the delay

with-outlosing data representativeness. Suchatechniquecanbe

veryusefultoachieveenergy-efficient and time-constrained

sensor networks ifthe application is not so dependent on

the dataprecisionorthe networkoperates inexception

situ-ation(e.g., fewresources remaining orurgent situation de-tection). Moreover, the proposed methodmeetsthedesign requirements in real-time WSNs.

As future work, we intend to better evaluate the

pro-posed technique by considering other network scenarios, andmatchingtheproposed application-level solution with lower-level ones, for example, by considering some

real-time-enabled routing protocol. We also planto apply the proposed methodtoprocessdata streamsalong the routing

task. Thus,notonly the data from a sourceis reduced, but

similar data from differentsourcesis also reduced, resulting

ina moreenergy-efficient solution.

References

[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and

E.Cayirci. A survey on sensornetworks. IEEE

Commu-nicationsMagazine, 40(8): 102-114, August 2002.

[2] L.S. Buriol, D. Donato, S. Leonardi, andT. Matzner.

Us-ing datastreamalgorithms for computing properties of large graphs. In Workshop on Massive Geometric Data Sets

(MASSIVE'05), Pisa, Italy,June 9 2005.

[3] T. H. Chan, C. K. Ki, and H. Ngan. Real-timesupportfor

wirelesssensornetworks. Unpublished,2005.

[4] J.Ledlie, C.Ng, D.A. Holland,K.-K. Muniswamy-Reddy,

U. Braun, and M. Seltzer. Provenance-aware sensordata

storage. In1stIEEEInternationalWorkshoponNetworking Meets Databases(NetDB), April2005.

[5] H. Li, P. J. Shenoy, and K. Ramamritham. Scheduling

com-municationinreal-timesensorapplications. In IEEE

Real-Time and Embedded Technology and Applications

Sympo-sium -(RTAS'04), pages 10-18, Toronto, Canada, 25-28 May 2004. IEEE,IEEEComputer Society.

[6] A.Lins, E. F.Nakamura, A. A.Loureiro,and C. J. Coelho

Jr. Beanwatcher: A toolto generate multimedia monitor-ing applications for wireless sensornetworks. InA. Mar-shall and N. Agoulmine, editors, Management of Multime-dia Networks andServices, volume 2839 of Lecture Notes inComputer Science,pages128-141, Belfast,Northern Ire-land, September 2003. Springer-Verlag Heidelberg. [7] A.Lins,E. F.Nakamura,A. A.Loureiro,and C. J. Coelho Jr.

Generating monitoring applications for wireless networks. InProceedings of the 9th IEEEInternational Conference

onEmerging TechnologiesandFactoryAutomation (ETFA

2003), Lisbon, Portugal, September2003.

[8] C. Lu, B. M. Blum, T. F Abdelzaher, J. A. Stankovic,

and T. He. Rap: Areal-time communication architecture for large-scale wireless sensor networks. In IEEE Real TimeTechnologyandApplications Symposium-(RTAS'02),

pages55-66, SanJose, CA, USA,24-27September2002. IEEE,IEEEComputer Society.

[9] S. R. Madden, M. J. Franklin, J. M. Hellerstein, and W.Hong. Tinydb: Anacquisitional queryprocessing sys-temfor sensornetworks. ACM Transactions onDatabase

Systems (TODS), 30(1):122-173,March 2005.

[10] S.Muthukrishnan. Data streams: Algorithms and

applica-tions. In 4th ACM-SIAMSymposiumonDiscretealgorithms,

Baltimore, Maryland, 2003.

[11] E. F.Nakamura, F G.Nakamura,C. M. S.Figueredo, and

A. A. F. Loureiro. Usinginformation fusiontoassist data dissemination in wirelesssensornetworks. Telecommunica-tionSystems, 30(1/2/3):237-254,November 2005.

[12] S. Siegel and J. N. John Castellan. Nonparametric Statis-ticsforthe Behavioral Sciences. McGraw-HillCollege,2nd editionedition, January1988.

* logn * n/2

o n