Distributed Algorithms for Message-Passing Systems PDF
Preview Distributed Algorithms for Message-Passing Systems
Michel Raynal Distributed Algorithms for Message-Passing Systems Distributed Algorithms for Message-Passing Systems Michel Raynal Distributed Algorithms for Message-Passing Systems MichelRaynal InstitutUniversitairedeFrance IRISA-ISTIC UniversitédeRennes1 RennesCedex France ISBN978-3-642-38122-5 ISBN978-3-642-38123-2(eBook) DOI10.1007/978-3-642-38123-2 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013942973 ACMComputingClassification(1998): F.1,D.1,B.3 ©Springer-VerlagBerlinHeidelberg2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Laprofusiondeschosescachaitlararetédesidéesetl’usuredescroyances. [...]Retenirquelquechosedutempsoùl’onneseraplus. InLesannées(2008),AnnieErnaux Nelmezzodelcammindinostravita Miritrovaiperunaselvaoscura, Chéladirittaviaerasmarritta. InLadivinacommedia(1307–1321),DanteAlighieri(1265–1321) Wirmüssennichtssein,sondernalleswerdenwollen. JohannWolfgangvonGoethe(1749–1832) Chaquegénération,sansdoute,secroitvouéeàrefairelemonde. Lamiennesaitpourtantqu’ellenelereferapas.Maissatâcheestpeut-êtreplusgrande. Elleconsisteàempêcherquelemondenesedéfasse. SpeechattheNobelBanquet,Stockholm,December10,1957,AlbertCamus(1913–1960) Rienn’estprécairecommevivre Riencommeêtren’estpassager C’estunpeufondrepourlegivre Oupourleventêtreléger J’arriveoùjesuisétranger. InLevoyagedeHollande(1965),LouisAragon(1897–1982) What Is Distributed Computing? Distributed computing was born in the late 1970s when researchers and practitioners started taking into account the intrinsic characteristicofphysicallydistributedsystems.Thefieldthenemergedasaspecial- ized research area distinct from networking, operating systems, and parallel com- puting. Distributed computing arises when one has to solve a problem in terms of dis- tributed entities (usually called processors, nodes, processes, actors, agents, sen- sors, peers, etc.) such that each entity has only a partial knowledge of the many parametersinvolvedintheproblemthathastobesolved.Whileparallelcomputing andreal-timecomputingcanbecharacterized,respectively,bythetermsefficiency andon-timecomputing,distributedcomputingcanbecharacterizedbythetermun- certainty. This uncertainty is created by asynchrony, multiplicity of control flows, v vi Preface absenceofsharedmemoryandglobaltime,failure,dynamicity,mobility,etc.Mas- tering one form or another of uncertainty is pervasive in all distributed computing problems.Amaindifficultyindesigningdistributedalgorithmscomesfromthefact thateachentitycooperatingintheachievementofacommongoalcannothavein- stantaneous knowledge of the current state of the other entities; it can only know theirpastlocalstates. Althoughdistributedalgorithmsareoftenmadeupofafewlines,theirbehavior can be difficult to understand and their properties hard to state and prove. Hence, distributedcomputingis notonlyafundamentaltopicbutalsoachallengingtopic wheresimplicity,elegance,andbeautyarefirst-classcitizens. WhyThisBook? Whiletherearealotofbooksonsequentialcomputing(bothon basic data structures, or algorithms), this is not the case in distributed computing. Most books on distributed computing consider advanced topics where the uncer- tainty inherent to distributed computing is created by the net effect of asynchrony andfailures.Itfollowsthatthesebooksaremoreappropriateforgraduatestudents thanforundergraduatestudents. Theaimofthisbookistopresentinacomprehensivewaybasicnotions,concepts andalgorithmsofdistributedcomputingwhenthedistributedentitiescooperateby sendingandreceivingmessagesontopofanunderlyingnetwork.Inthiscase,the main difficulty comes from the physical distribution of the entities and the asyn- chronyoftheenvironmentinwhichtheyevolve. Audience This book has been written primarily for people who are not familiar withthetopicandtheconceptsthatarepresented.Theseincludemainly: • Senior-level undergraduate students and graduate students in computer science orcomputerengineering,whoareinterestedintheprinciplesandfoundationsof distributedcomputing. • Practitionersandengineerswhowanttobeawareofthestate-of-the-artconcepts, basicprinciples,mechanisms,andtechniquesencounteredindistributedcomput- ing. Prerequisites for this book include undergraduate courses on algorithms, and ba- sic knowledgeon operatingsystems. Selectionsof chaptersfor undergraduateand graduatecoursesaresuggestedinthesectiontitled“HowtoUseThisBook”inthe Afterword. Content Asalreadyindicated,thisbookcoversalgorithms,basicprinciples,and foundations of message-passing programming, i.e., programs where the entities communicatebysendingandreceivingmessagesthroughanetwork.Theworldis distributed,andthealgorithmicthinkingsuitedtodistributedapplicationsandsys- temsisnotreducibletosequentialcomputing.Knowledgeofthebasesofdistributed computingisbecomingmoreimportantthaneverasmoreandmorecomputerap- plicationsarenowdistributed.Thebookiscomposedofsixparts. Preface vii • Theaimofthefirstpart,whichismadeupofsixchapters,istogiveafeelforthe natureofdistributedalgorithms,i.e.,whatmakesthemdifferentfromsequential or parallel algorithms. To that end, it mainly considers distributed graph algo- rithms.Inthiscontext,eachnodeofthegraphisaprocess,whichhastocompute aresultwhosemeaningdependsonthewholegraph. Basic distributed algorithms such as network traversals, shortest-path algo- rithms, vertex coloring, knot detection, etc., are first presented. Then, a general frameworkfordistributedgraphalgorithmsisintroduced.Achapterisdevotedto leaderelectionalgorithmsonaringnetwork,andanotherchapterfocusesonthe navigationofanetworkbymobileobjects. • Thesecondpartisonthenatureofdistributedexecutions.Itismadeupoffour chapters.Insomesense,thispartisthecoreofthebook.Itexplainswhatadis- tributedexecutionis,thefundamentalnotionofaconsistentglobalstate,andthe impossibility—without freezing the computation—of knowing whether a com- putedconsistentglobalstatehasbeenpassedthroughbytheexecutionornot. Then,thispartofthebookaddressesanimportantissueofdistributedcompu- tations, namely the notion of logical time: scalar (linear) time, vector time, and matrixtime.Eachtypeoftimeisanalyzedandexamplesoftheirusesaregiven. A chapter, which extends the notion of a global state, is then devoted to asyn- chronous distributed checkpointing. Finally, the last chapter of this part shows how to simulate a synchronous system on top of an asynchronous system (such simulatorsarecalledsynchronizers). • The third part of the book is made up of two chapters devoted to distributed mutual exclusion and distributed resource allocation. Different families of permission-based mutual exclusion algorithms are presented. The notion of an adaptivealgorithmisalsointroduced.Thenotionofacriticalsectionwithmul- tiple entries, and the case of resources with a single or several instances is also presented.Associateddeadlockpreventiontechniquesareintroduced. • Thefourthpartofthebookisonthedefinitionandtheimplementationofcommu- nicationoperationswhoseabstractionlevelishigherthanthesimplesend/receive ofmessages.Thesecommunicationabstractionsimposeorderconstraintsonmes- sage deliveries. Causal message delivery and total order broadcast are first pre- sentedinonechapter.Then,anotherchapterconsiderssynchronouscommunica- tion(alsocalledrendezvousorlogicallyinstantaneouscommunication). • Thefifthpartofthebook,whichismadeupoftwochapters,isonthedetection ofstablepropertiesencounteredindistributedcomputing.Astablepropertyisa propertythat,oncetrue,remainstrueforever.Thepropertieswhicharestudiedare thedetectionoftheterminationofadistributedcomputation,andthedetectionof distributeddeadlock.Thispartofthebookisstronglyrelatedtothesecondpart (whichisdevotedtothenotionofaglobalstate). • The sixth and last part of the book, which is also made up of two chapters, is devoted to the notion of a distributed shared memory. The aim is here to pro- videtheentities(processes)withasetofobjectsthatallowthemtocooperateat viii Preface anabstractionlevelmoreappropriatethantheuseofmessages.Twoconsistency conditions,whichcanbeassociatedwiththeseobjects,arepresentedandinves- tigated,namely,atomicity(alsocalledlinearizability)andsequentialconsistency. Severalalgorithmsimplementingtheseconsistencyconditionsaredescribed. Tohaveamorecompletefeelingofthespiritofthisbook,thereaderis invited to consult the section “The Aim of This Book” in the Afterword, which describes what it is hoped has been learned from this book. Each chapter starts with a short presentationandalistofthemainkeywords,andterminateswithasummaryofits content.Eachofthesixpartsofthebookisalsointroducedbyabriefdescriptionof itsaimanditstechnicalcontent. Acknowledgments Thisbookoriginatesfromlecturenotesforundergraduateandgraduate coursesondistributedcomputingthatIgiveattheUniversityofRennes(France)and,asan invitedprofessor,atseveraluniversitiesallovertheworld.Iwouldliketothankthestudents fortheirquestionsthat,inonewayoranother,havecontributedtothisbook.Iwantalsoto thankRonanNugent(Springer)forhissupportandhishelpinputtingitalltogether. Lastbutnotleast(andmaybemostimportantly),Ialsowanttothankalltheresearchers whoseresultsarepresentedinthisbook.Withouttheirwork,thisbookwouldnotexist. MichelRaynal ProfesseurdesUniversités InstitutUniversitairedeFrance IRISA-ISTIC,UniversitédeRennes1 CampusdeBeaulieu,35042,Rennes,France March–October2012 Rennes,Saint-Grégoire,Tokyo,Fukuoka(AINA’12),Arequipa(LATIN’12), Reykjavik(SIROCCO’12),Palermo(CISIS’12),Madeira(PODC’12),Lisbon, Douelle,Saint-Philibert,RhodesIsland(Europar’12), SalvadordeBahia(DISC’12),MexicoCity(TuringYearatUNAM) Contents PartI DistributedGraphAlgorithms 1 BasicDefinitionsandNetworkTraversalAlgorithms . . . . . . . . . 3 1.1 DistributedAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 AnIntroductoryExample: LearningtheCommunicationGraph . . . . . . . . . . . . 6 1.2 ParallelTraversal:BroadcastandConvergecast . . . . . . . . . . . 9 1.2.1 BroadcastandConvergecast . . . . . . . . . . . . . . . . . 9 1.2.2 AFloodingAlgorithm . . . . . . . . . . . . . . . . . . . . 10 1.2.3 Broadcast/ConvergecastBasedonaRootedSpanningTree 10 1.2.4 BuildingaSpanningTree . . . . . . . . . . . . . . . . . . 12 1.3 Breadth-FirstSpanningTree . . . . . . . . . . . . . . . . . . . . . 16 1.3.1 Breadth-FirstSpanningTree BuiltWithoutCentralizedControl. . . . . . . . . . . . . . 17 1.3.2 Breadth-FirstSpanningTreeBuiltwithCentralizedControl 20 1.4 Depth-FirstTraversal . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.1 ASimpleAlgorithm . . . . . . . . . . . . . . . . . . . . . 24 1.4.2 Application:ConstructionofaLogicalRing . . . . . . . . 27 1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6 BibliographicNotes . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.7 ExercisesandProblems . . . . . . . . . . . . . . . . . . . . . . . 33 2 DistributedGraphAlgorithms . . . . . . . . . . . . . . . . . . . . . 35 2.1 DistributedShortestPathAlgorithms . . . . . . . . . . . . . . . . 35 2.1.1 ADistributedAdaptation ofBellman–Ford’sShortestPathAlgorithm . . . . . . . . 35 2.1.2 ADistributedAdaptation ofFloyd–Warshall’sShortestPathsAlgorithm . . . . . . . 38 2.2 VertexColoringandMaximalIndependentSet . . . . . . . . . . . 42 2.2.1 OnSequentialVertexColoring . . . . . . . . . . . . . . . 42 ix x Contents 2.2.2 Distributed((cid:2)+1)-ColoringofProcesses . . . . . . . . . 43 2.2.3 ComputingaMaximalIndependentSet . . . . . . . . . . . 46 2.3 KnotandCycleDetection . . . . . . . . . . . . . . . . . . . . . . 50 2.3.1 DirectedGraph,Knot,andCycle . . . . . . . . . . . . . . 50 2.3.2 Communication Graph, Logical Directed Graph, andReachability . . . . . . . . . . . . . . . . . . . . . . . 51 2.3.3 SpecificationoftheKnotDetectionProblem . . . . . . . . 51 2.3.4 PrincipleoftheKnot/CycleDetectionAlgorithm . . . . . . 52 2.3.5 LocalVariables . . . . . . . . . . . . . . . . . . . . . . . 53 2.3.6 BehaviorofaProcess . . . . . . . . . . . . . . . . . . . . 54 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.5 BibliographicNotes . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.6 ExercisesandProblems . . . . . . . . . . . . . . . . . . . . . . . 58 3 AnAlgorithmicFramework toComputeGlobalFunctionsonaProcessGraph. . . . . . . . . . . 59 3.1 DistributedComputationofGlobalFunctions. . . . . . . . . . . . 59 3.1.1 TypeofGlobalFunctions . . . . . . . . . . . . . . . . . . 59 3.1.2 ConstraintsontheComputation . . . . . . . . . . . . . . . 60 3.2 AnAlgorithmicFramework . . . . . . . . . . . . . . . . . . . . . 61 3.2.1 ARound-BasedFramework . . . . . . . . . . . . . . . . . 61 3.2.2 WhentheDiameterIsNotKnown . . . . . . . . . . . . . 64 3.3 DistributedDeterminationofCutVertices . . . . . . . . . . . . . 66 3.3.1 CutVertices . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3.2 AnAlgorithmDeterminingCutVertices . . . . . . . . . . 67 3.4 ImprovingtheFramework . . . . . . . . . . . . . . . . . . . . . . 69 3.4.1 TwoTypesofFiltering . . . . . . . . . . . . . . . . . . . . 69 3.4.2 AnImprovedAlgorithm . . . . . . . . . . . . . . . . . . . 70 3.5 TheCaseofRegularCommunicationGraphs . . . . . . . . . . . . 72 3.5.1 TradeoffBetweenGraphTopologyandNumberofRounds 72 3.5.2 DeBruijnGraphs . . . . . . . . . . . . . . . . . . . . . . 73 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.7 BibliographicNotes . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.8 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4 LeaderElectionAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 TheLeaderElectionProblem . . . . . . . . . . . . . . . . . . . . 77 4.1.1 ProblemDefinition. . . . . . . . . . . . . . . . . . . . . . 77 4.1.2 AnonymousSystems:AnImpossibilityResult . . . . . . . 78 4.1.3 BasicAssumptionsandPrinciples oftheElectionAlgorithms. . . . . . . . . . . . . . . . . . 79 4.2 ASimpleO(n2)LeaderElectionAlgorithm forUnidirectionalRings . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.1 ContextandPrinciple . . . . . . . . . . . . . . . . . . . . 79 4.2.2 TheAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.3 TimeCostoftheAlgorithm . . . . . . . . . . . . . . . . . 80
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