Inthispaperweproposeasufficientconditionforminimalroutingin3-dimensional(3-D)mesheswithfaultynodes.Itisbasedonanearlyworkoftheauthoronminimalroutingin2-dimensional(2-D)meshes.Unlikemanytraditionalmodelsthatassumeallthenodesknowglobalfaultdistributionorjustadjacentfaultinformation,ourapproachisbasedontheconceptoflimitedglobalfaultinformation.First,weproposeafaultmodelcalledfaultycubeinwhichallfaultynodesinthesystemarecontainedinasetoffaultycubes.Faultinformationisthendistributedtolimitednumberofnodeswhileitisstillsufficienttosupportminimalrouting.Thelimitedfaultinformationcollectedateachnodeisrepresentedbyavectorcalledextendedsafetylevel.Theextendedsafetylevelassociatedwithanodecanbeusedtodeterminetheexistenceofaminimalpathfromthisnodetoagivendestination.Specifically,westudytheexistenceofminimalpathsatagivensourcenode,limiteddistributionoffaultinformation,minimalrouting,anddeadlock-freeandlivelock-freerouting.Ourresultsshowthatanyminimalroutingthatispartiallyadaptivecanbeappliedinourmodelaslongasthedestinationnodemeetsacertaincondition.Wealsoproposeadynamicplanar-adaptiveroutingschemethatoffersbetterfaulttoleranceandadaptivitythantheplanar-adaptiveroutingschemein3-Dmeshes.Ourapproachisthefirstattempttoaddressadaptiveandminimalroutingin3-Dmesheswithfaultynodesusinglimitedfaultinformation.
