distributed systems tree and flood algorithms...distributed systems tree and flood algorithms rik...

DistributedSystems

TreeandFloodAlgorithmsRikSarkar

UniversityofEdinburgh

2016/2017

DistributedComputaEon

•  Howtosendmessagestoallnodesefficiently•  Howtocomputesumsofvaluesatallnodesefficiently

•  BroadcasEngmessages•  CompuEngsumsinatree•  CompuEngtreesinanetwork

DistributedSystems,Edinburgh,2016

Ref:NL

Networkasagraph

•  Diameter–  Themaximumdistancebetween2nodesinthenetwork

•  Radius–  Halfthediameter

•  Spanningtreeofagraph:–  Asubgraphwhichisatree,andreachesallnodesofthegraph

–  Ifnetworkhasnnodes•  Howmanyedgesdoesaspanningtreehave?


CompuEngsumsinatree

•  Supposerootwantstoknowsumofvaluesatallnodes


root

CompuEngsumsinatree•  Supposerootwantstoknowsumofvaluesatallnodes

•  Itsends“compute”messagetoallchildren

•  Theyforwardthemessagetoalltheirchildren(unlessitisaleafnode)

•  Thevaluesmoveupwardfromleaves

•  Eachnodeaddsvaluesfromallchildrenanditsownvalue

•  Sendsittoitsparent


root

CompuEngsumsinatree

•  Whatcanyoucomputeotherthansums?

•  Howmanymessagesdoesittake?

•  HowmuchEmedoesittake?


root

GlobalMessagebroadcast•  Messagemustreachallnodesinthenetwork– DifferentfrombroadcasttransmissioninLAN– Allnodesinalargenetworkcannotbereachedwithsingletransmission


Source

GlobalMessagebroadcast•  Messagemustreachallnodesinthenetwork– DifferentfrombroadcasttransmissioninLAN– Allnodesinalargenetworkcannotbereachedwithsingletransmissions


Source

FloodingforBroadcast

•  ThesourcesendsaFloodmessagetoallneighbors

•  Themessagehas– TypeFlood– Uniqueid:(sourceid,messageseq)– Data


FloodingforBroadcast

•  ThesourcesendsaFloodmessage,withauniquemessageidtoallneighbors

•  Everynodepthatreceivesafloodmessagem,doesthefollowing:–  Ifm.idwasseenbefore,discardm– Otherwise,Addm.idtolistofpreviouslyseenmessagesandsendmtoallneighborsofp


Floodingforbroadcast

•  Storage– Eachnodeneedstostorealistoffloodidsseenbefore

–  Ifaprotocolrequiresxfloods,theneachnodemuststorexids•  (thereisawaytoreducethis.Think!)


AssumpEons

•  Weareassuming:– NodesareworkinginsynchronouscommunicaDonrounds(e.g.transmissionsoccurinintervalsof1secondexactly)

– MessagesfromallneighborsarriveatthesameEme,andprocessedtogether

–  Ineachround,eachnodecansuccessfullysend1messagetoeachneighbor

– AnynecessarycomputaEoncanbecompletedbeforethenextround


CommunicaEoncomplexity

•  Themessage/communicaEoncomplexityis:



•  Thethemessage/communicaEoncomplexityis:– O(|E|)



•  Thethemessage/communicaEoncomplexityis:– O(|E|)– Worstcase:O(n2)


ReducingCommunicaEoncomplexity(slightly)

•  Nodepneednotsendmessagemtoanynodefromwhichithasalreadyreceivedm– Needstokeeptrackofwhichnodeshavesentthemessage

– Savessomemessages– DoesnotchangeasymptoEccomplexity


Timecomplexity

•  Thenumberofroundsneededtoreachallnodes:diameterofG


CompuEngTreefromanetwork

•  BFStree– TheBreadthfirstsearchtree– Withaspecifiedrootnode


BFSTree

•  Breadthfirstsearchtree– Everynodehasaparentpointer– Andzeroormorechildpointers

– BFSTreeconstrucEonalgorithmsetsthesepointers


BFSTreeConstrucEonalgorithm•  Breadthfirstsearchtree–  Theroot(source)nodedecidestoconstructatree– Usesfloodingtoconstructatree–  Everynodepongebngthemessageforwardstoallneighbors

– AddiEonally,everynodepstoresparentpointer:nodefromwhichitfirstreceivedthemessage•  IfmulEpleneighborshadfirstsentpthemessageinthesameround,chooseparentarbitrarily.E.g.nodewithsmallestid

–  pinformsitsparentoftheselecEon•  Parentcreatesachildpointertop


BFSTree

•  Property:BFStreeisashortestpathtree– Forsourcesandanynodep– TheshortestpathbetweensandpiscontainedintheBFStree


Time&messagecomplexity

•  AsymptoEcallySameasFlooding


root

Treebasedbroadcast

•  Sendmessagetoallnodesusingtree– BFStreeisaspanningtree:connectsallnodes

•  Floodingonthetree

•  Receivemessagefromparent,sendtochildren


root

Treebasedbroadcast

•  Simplerthanflooding:sendmessagetoallchildren

•  CommunicaEon:Numberofedgesinspanningtree:n-1


AggregaEon:Findthesumofvaluesatallnodes

•  WithBFStree

•  Startfromleafnodes– Nodeswithoutchildren– Sendthevaluetoparent

•  Everyothernode:– Waitforallchildrentoreport– Sumvaluesfromchildren+ownvalue– Sendtoparent


AggregaEon

•  Withoutthetree•  Floodfromallnodes:– O(|E|)costpernode– O(n*|E|)totalcost:expensive– Eachnodeneedstostorefloodidsfromnnodes•  RequiresΩ(n)storageateachnode

– Goodfaulttolerance•  IfafewnodesfailduringoperaEon,alltherestsEllgetsomevalue


AggregaEon

•  WithTree

•  AlsocalledConvergecast


AggregaEon•  WithTree

•  Oncetreeisbuilt,anynodecanuseforbroadcast–  Justfloodonthetree

•  Anynodecanuseforconvergecast–  FirstfloodamessageonthetreerequesEngdata– Nodesstoreparentpointer–  Thenreceivedata

•  WhatisthedrawbackoftreebasedaggregaEon?


AggregaEon•  WithTree

•  Oncetreeisbuilt,anynodecanuseforbroadcast–  Justfloodonthetree

•  Anynodecanuseforconvergecast–  FirstfloodamessageonthetreerequesEngdata–  Nodesstoreparentpointer–  Thenreceivedata

•  Faulttolerancenotverygood–  Ifanodefails,themessagesinitssubtreewillbelost–  WillneedtorebuildthetreeforfutureoperaEons


CompuEngTrees:

•  Whatiftheedgeshaveweights?


AggregaEonusingTrees:

•  Whatiftheedgeshaveweights?•  ThecostmaynotbeO(n)sinceweightscanbehigher

•  Howtogetthebestperformance?


Minimumspanningtreeis

•  Aspanningtree(reachesallnodes)•  Withminimumpossibletotalweight

•  Howcanwecomputeaminimumspanningtreeefficientlyinadistributedsystem?

•  (remember,anodeknowsonlyitsneighborsandedgeweights)


distributed systems tree and flood algorithms...distributed systems tree and flood algorithms rik...

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