2024年3月16日发(作者：沃尔沃xc90降价严重为什么)

Ef?cientIn?uenceMaximizationinSocialNetworks

MicrosoftResearchAsia

Beijing,China

WeiChen

weic@unw@

MicrosoftResearchAsia

Beijing,China

YajunWang

uterScience

TsinghuaUniversity

Beijing,China

SiyuYang

@

ABSTRACT

In?uencemaximizationistheproblemof?ndingasmallsubset

ofnodes(seednodes)inasocialnetworkthatcouldmaximizethe

spreadofin?paper,westudytheef?cientin?uence

oim-

provetheoriginalgreedyalgorithmof[5]anditsimprovement[7]

tofurtherreduceitsrunningtime,andthesecondistoproposenew

degreediscountheuristicsthatimprovesin?-

uateouralgorithmsbyexperimentsontwolargeacademiccollabo-

.

Ourexperimentalresultsshowthat(a)ourimprovedgreedyalgo-

rithmachievesbetterrunningtimecomparingwiththeimprove-

mentof[7]withmatchingin?uencespread,(b)ourdegreediscount

heuristicsachievemuchbetterin?uencespreadthanclassicdegree

andcentrality-basedheuristics,andwhentunedforaspeci?cin?u-

encecascademodel,itachievesalmostmatchingin?uencethread

withthegreedyalgorithm,andmoreimportantly(c)thedegreedis-

countheuristicsrunonlyinmillisecondswhileeventheimproved

greedyalgorithmsruninhoursinourexperimentgraphswithafew

tensofthousandsofnodes.

Basedonourresults,webelievethat?ne-tunedheuristicsmay

providetrulyscalablesolutionstothein?uencemaximizationprob-

lemwithsatisfyingin?uencespreadandblazinglyfastrunning

ore,contrarytowhatimpliedbytheconclusionof[5]

thattraditionalheuristicsareoutperformedbythegreedyapprox-

imationalgorithm,ourresultsshednewlightsontheresearchof

heuristicalgorithms.

UCTION

CategoriesandSubjectDescriptors

F.2.2[AnalysisofAlgorithmsandProblemComplexity]:Non-

numericalAlgorithmsandProblems

GeneralTerms

Algorithms,Experimentation,Performance

Keywords

socialnetworks,in?uencemaximization,heuristicalgorithms

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permissionand/orafee.

KDD’09,June28–July1,2009,Paris,France.

Copyright2009ACM978-1-60558-495-9/$5.00.

Recentlymanylarge-scaleonlinesocialnetworksites,suchas

FacebookandFriendster,becomesuccessfulbecausetheyarevery

effectivetoolsinconnectingpeopleandbringingsmallanddiscon-

nectedof?er,theyarealso

becomingahugedisseminationandmarketingplatform,allowing

informationandideastoin?uencealargepopulationinashortpe-

r,tofullyutilizethesesocialnetworksasmar-

ketingandinformationdisseminationplatforms,manychallenges

paper,wepresentourworktowardsaddress-

ingoneofthechallenges,namely?ndingin?uentialindividuals

ef?cientlyinalarge-scalesocialnetwork.

Considerthefollowinghypotheticalscenarioasamotivatingex-

companydevelopsacoolonlineapplicationfor

anonlinesocialnetworkandwantstomarketitthroughthesame

limitedbudgetsuchthatitcanonlyselectasmall

numberofinitialusersinthenetworktouseit(bygivingthemgifts

orpayments).Thecompanywishesthattheseinitialuserswould

lovetheapplicationandstartin?uencingtheirfriendsonthesocial

networktouseit,andtheirfriendswouldin?uencetheirfriends’

friendsandsoon,andthusthroughtheword-of-moutheffecta

largepopulationinthesocialnetworkwouldadopttheapplication.

Theproblemiswhomtoselectastheinitialuserssothattheyeven-

tuallyin?,

theproblemof?ndingin?uentialindividualsinasocialnetwork.

Thisproblem,referredtoasin?uencemaximization,wouldbe

ofinteresttomanycompaniesaswellasindividualsthatwantto

promotetheirproducts,services,andinnovativeideasthroughthe

powerfulword-of-moutheffect(orcalledviralmarketing).Online

socialnetworksprovidegoodopportunitiestoaddressthisprob-

lem,becausetheyareconnectingahugenumberofpeopleand

theycollectahugeamountofinformationaboutthesocialnet-

r,theyalso

ialnetworksare

large-scale,havecomplexconnectionstructures,andarealsovery

dynamic,whichmeansthatthesolutiontotheproblemneedstobe

veryef?cientandscalable.

DomingosandRichardson[3,8]arethe?rsttostudyin?uence

ethodsareproba-

bilistic,,Kleinberg,andTardos[5]arethe?rstto

formulatetheproblemasthefollowingdiscreteoptimizationprob-

lnetworkismodeledasagraphwithverticesrep-

resentingindividualsandedgesrepresentingconnectionsorrela-

?uencearepropagatedinthe

ascade

models,namelytheindependentcascademodel,theweightcas-

cademodel,andthelinearthresholdmodel,areconsideredin[5].

Givenasocialnetworkgraph,aspeci?cin?uencecascademodel,

199

andasmallnumberk,thein?uencemaximizationproblemisto

?ndkverticesinthegraph(referedtoasseeds)suchthatunder

thein?uencecascademodel,theexpectednumberofverticesin-

?uencedbythekseeds(referredtoasthein?uencespreadinthe

paper)isthelargestpossible.

hattheoptimizationproblemisNP-hard,and

presentagreedyapproximationalgorithmapplicabletoallthree

models,whichguaranteesthatthein?uencespreadiswithin(1?

1/e)oftheoptimalin?soshowthroughex-

perimentsthattheirgreedyalgorithmsigni?cantlyoutperformsthe

classicdegreeandcentrality-basedheuristicsinin?uencespread.

However,theiralgorithmhasaseriousdrawback,whichisitsef-

?ementoftheirgreedyalgorithmistocomputethe

in?uencespreadgivenaseedset,whichturnsouttobeadif?cult

dof?ndinganexactalgorithm,theyrunMonte-Carlo

simulationsofthein?uencecascademodelforsuf?cientlymany

timestoobtainanaccurateestimateofthein?

result,even?ndingasmallseedsetinamoderatelylargenetwork

(e.g.15000vertices)couldtakedaystocompleteonamodern

servermachine.

Severalrecentstudiesaimedataddressingthisef?ciencyissue.

In[6],KimuraandSaitoproposeshortest-pathbasedin?uencecas-

cademodelsandprovideef?cientalgorithmsofcomputein?uence

r,sincethein?uencecascade

modelsaredifferent,theydonotdirectlyaddresstheef?ciencyis-

sueofthegreedyalgorithmsforthecascademodelsstudiedin[5].

In[7],tanoptimizationinselectingnew

seeds,whichisreferredtoasthe“Cost-EffectiveLazyForward”

(CELF)Foptimizationusesthesubmodular-

itypropertyofthein?uencemaximizationobjectivetogreatlyre-

ducethenumberofevaluationsonthein?uencespreadofver-

xperimentalresultsdemonstratethatCELFoptimiza-

tioncouldachieveasmuchas700timesspeedupinselectingseed

vertices,r,ourexperi-

mentsshowthattheimprovedalgorithmstilltakesafewhoursto

completeinagraphwithafewtensofthousandsofvertices,soit

isstillnotef?cientforlarge-scalenetworks.

Inthispaper,wetackletheef?ciencyissueofin?uencemaxi-

irection,we

designnewschemestofurtherimprovethegreedyalgorithm,and

combineourschemetogetherwiththeCELFoptimizationtoobtain

therdirection,weproposenew

degreediscountheuristicswithin?uencespreadsthataresigni?-

cantlybetterthantheclassicdegreeandcentrality-basedheuristics

andareclosetothein?

biggestadvantageofourheuristicsistheirspeed,astheyaremany

ordersofmagnitudefasterthanallgreedyalgorithms.

Ournewgreedyalgorithmsanddegreediscountheuristicsare

derivedfromtheindependentcascademodelandweightedcas-

uctextensiveexperimentsontworeal-life

collaborationnetworkstocompareouralgorithmswiththeCELF

optimizedalgorithmaswellasclassicdegreeandcentralityheuris-

metricswecomparearein?uencespreadandrunning

newgreedyalgorithms,theirin?uencespreadexactly

matchwiththeoriginalgreedyalgorithm,whereastheirrunning

timesare15%to34%

degreediscountheuristics,theirin?uencespreadareclosetothat

ofthegreedyalgorithm,andalwaysoutperformstheclassicdegree

ticularheuristictunedfor

theindependentcascademodelwithasmallpropagationprobabil-

ityalmostmatchesthein?uencespreadofthegreedyalgorithm

(sameasthegreedyalgorithminoneexperimentalgraphand3.4%

lowerinanothergraph)

biggestadvantageistheirblazinglyfastspeed—theycompletethe

taskinonlyafewmilliseconds,whichislessthanone-millionthof

rmore,wealsorunour

resultsdemonstratethatournewalgorithmsstillhavegoodin?u-

ore,

theyarerobustacrossthesemodels.

Theseresultsprovideusanewperspectiveinthestudyofthe

in?doffocusingoureffortin

furtherimprovingtherunningtimeofthegreedyalgorithm,itper-

hapsmorepromisingtofocusonimprovingheuristicsthatcould

beamilliontimesfasterandmakingtheirin?uencespreadcloseto

thegreedyalgorithm.

Tosummarize,,we

providefurtherimprovementtothegreedyalgorithmthathasguar-

anteedapproximatein?,andmoreimpor-

tantly,weproposenewheuristicsthathavein?uencespreadsclose

tothegreedyalgorithmwhilerunningatmorethansixordersof

agedbythese

results,wesuggestthatthepromisingapproachinsolvingthein-

?uencemaximizationproblemforlarge-scalesocialnetworksisto

investinheuristicstoimprovetheirin?uencespread,ratherthan

tryingtoimprovetherunningtimeofthegreedyalgorithms,which

istheapproachtakenbymostpreviousstudies.

n2presents

thegreedyalgorithmandournewimprovementstothegreedyalgo-

rithmintheindependentcascademodelandtheweightedcascade

n4

ludethepaperinSection5.

INGTHEGREEDY

ALGORITHM

Inthissection,wediscussimprovementofthegreedyalgorithm

proposedbyKempe,etal.[5]fortheindependentcascademodel

aswellastheweightedcascademodel.

2.1Problemde?nitionandthegreedy

algorithm

AsocialnetworkismodeledasanundirectedgraphG=(V,E),

withverticesinVmodelingtheindividualsinthenetworkand

-

ample,inourexperimentsection,westudycoauthorshipgraphs

whereverticesareauthorsofacademicpapersandtwovertices

haveanedgeifthetwocorrespondingauthorshavecoauthoreda

paper.

1

Weusentodenotethenumberofverticesandmtode-

venience,

Table1listsimportantvariablesusedthroughoutthepaper.

LetSbethesubsetofverticesselectedtoinitiatethein?uence

propagation,Cas(S)denote

therandomprocessofin?uencecascadefromtheseedsetS,of

whichtheoutputisarandomsetofverticesin?-

rithmsinthispapertakethegraphGandanumberkasinputand

generateaseedsetSofcardinalityk,withtheintentionthatthe

expectednumberofverticesin?uencedbytheseedsetS,which

wecallin?uencespread,isaslargeaspossible.

Ourcoauthorshipgraphsstudiedintheexperimentsectionareac-

tuallymultigraphs,withparalleledgesbetweentwoverticesdenot-

ingthenumberofpaperscoauthoredbythetwoauthors,sameas

in[5].Forsimplicity,however,inourexplanationofthealgorithms

andheuristics,ultscan

begeneralizedtomultigraphsinastraightforwardway.

1

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