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1、AnOptimalSolutionforByzantineAgreementunderaHierarchicalCluster-orientedMobileAd-hocNetworkShun-ShengWang,Kuo-QinYan*,andShu-ChingWang*ChaoyangUniversityofTechnology168,JifongE.Rd.,WufongTownship,TaichungCounty41349,Taiwan,R.O.C.Email:{sswang;kqyan*;scwang
2、*}@cyut.edu.tw*Correspondingauthortoprovidephone:+886-4-2330-000;fax:+886-2330-4902AbstractMobileAdhocNETworks(MANETs)arebecomingmorepopularduetotheadvantagethattheydonotrequireanyfixedinfrastructure,andthatcommunicationamongprocessorscanbeestablishedquick
3、ly.Forthisreason,potentialMANETapplicationsincludemilitaryuses,searchandrescueandmeetingsorconferences.Therefore,thefault-toleranceandreliabilityoftheMANETisanimportantissue,whichneedstobeconsidered.Theproblemofreachingagreementinthedistributedsystemisoneo
4、fthemostimportantareasofresearchtodesignafault-tolerantsystem.Withanagreement,eachcorrectprocessorcancopewiththeinfluencefromotherfaultycomponentsinthenetworktoprovideareliablesolution.Inthisresearch,apotentialMANETwithadualfailuremodeisconsidered.Thepropo
5、sedprotocolcanusetheminimumnumberofroundsofmessageexchangetoreachacommonagreementandcantolerateamaximumnumberofallowablefaultycomponentstoinduceallcorrectprocessorstoreachacommonagreementwithintheMANET.Keywords:ByzantineAgreementProblem,MobileAd-hocNetwork
6、,DistributedSystem,Fault-Tolerance,DualFailureModes.1.IntroductionAdistributedcomputingsystemiscomposedofasetofprocessors,whichcommunicatewitheachotherthroughthenetwork.Areliablecomputersystemneedstocopewiththefaultsorinterferencefromotherfaultycomponents.
7、Inmanycases,reachinganagreementinthepresenceofmalfunctioningcomponentsisthecentralissueoffault-toleratedistributedcomputing[2,7].SuchageneralproblemiscalledtheByzantineAgreement(BA)problemandwasfirststudiedbyLamport[7].Traditionally,theBAproblemdefinedbyLa
8、mportassumesthefollowing[7]:(1)Therearenprocessors,ofwhichatmosttp(tp≤(n-1)/3)processorscouldfailwithoutbreakingdownaworkablenetwork.(2)Theprocessorscommunicatewitheachotherthroughmessageexchangesinafullyco
