Michel Raynal. Distributed Algorithms for Message-Passing Systems

Size: px

Start display at page:

Download "Michel Raynal. Distributed Algorithms for Message-Passing Systems"

Fay Reynolds
5 years ago
Views:

1 Michel Raynal Distributed Algorithms for Message-Passing Systems

2 Contents Part I Distributed Graph Algorithms 1 Basic Definitions and Network Traversal Algorithms DistributedAlgorithms Definition An Introductory Example: LearningtheCommunicationGraph Parallel Traversal: Broadcast and Convergecast Broadcast and Convergecast A Flooding Algorithm Broadcast/Convergecast Based on a Rooted Spanning Tree Building a Spanning Tree Breadth-First Spanning Tree Breadth-First Spanning Tree Built Without Centralized Control Breadth-First Spanning Tree Built with Centralized Control Depth-FirstTraversal ASimpleAlgorithm Application:ConstructionofaLogicalRing Summary Bibliographic Notes ExercisesandProblems Distributed Graph Algorithms Distributed Shortest Path Algorithms A Distributed Adaptation of Bellman Ford s Shortest Path Algorithm A Distributed Adaptation of Floyd Warshall s Shortest Paths Algorithm Vertex Coloring and Maximal Independent Set On Sequential Vertex Coloring ix

3 x Contents Distributed ( + 1)-ColoringofProcesses Computing a Maximal Independent Set KnotandCycleDetection Directed Graph, Knot, and Cycle Communication Graph, Logical Directed Graph, and Reachability Specification of the Knot Detection Problem PrincipleoftheKnot/CycleDetectionAlgorithm Local Variables Behavior of a Process Summary Bibliographic Notes ExercisesandProblems An Algorithmic Framework to Compute Global Functions on a Process Graph Distributed Computation of Global Functions Type of Global Functions ConstraintsontheComputation AnAlgorithmicFramework A Round-Based Framework WhentheDiameterIsNotKnown DistributedDeterminationofCutVertices CutVertices AnAlgorithmDeterminingCutVertices ImprovingtheFramework Two Types of Filtering AnImprovedAlgorithm The Case of Regular Communication Graphs Tradeoff Between Graph Topology and Number of Rounds De Bruijn Graphs Summary Bibliographic Notes Problem Leader Election Algorithms The Leader Election Problem Problem Definition Anonymous Systems: An Impossibility Result Basic Assumptions and Principles oftheelectionalgorithms A Simple O(n 2 ) Leader Election Algorithm for Unidirectional Rings ContextandPrinciple TheAlgorithm TimeCostoftheAlgorithm... 80

4 Contents xi MessageCostoftheAlgorithm ASimpleVariant An O(nlog n) Leader Election Algorithm for Bidirectional Rings ContextandPrinciple TheAlgorithm Time and Message Complexities An O(nlog n) Election Algorithm for Unidirectional Rings ContextandPrinciples TheAlgorithm Discussion: Message Complexity and FIFO Channels TwoParticularCases Summary Bibliographic Notes ExercisesandProblems Mobile Objects Navigating a Network Mobile Object in a Process Graph Problem Definition MobileObjectVersusMutualExclusion ACentralized(Home-Based)Algorithm The Algorithms Presented in This Chapter ANavigationAlgorithmforaCompleteNetwork Underlying Principles TheAlgorithm A Navigation Algorithm Based on a Spanning Tree Principles of the Algorithm: TreeInvariantandProxyBehavior TheAlgorithm Discussion and Properties ProofoftheAlgorithm An Adaptive Navigation Algorithm The Adaptivity Property PrincipleoftheImplementation An Adaptive Algorithm Based on a Distributed Queue Properties ExampleofanExecution Summary Bibliographic Notes ExercisesandProblems Part II Logical Time and Global States in Distributed Systems 6 Nature of Distributed Computations and the Concept of a Global State A Distributed Execution Is a Partial Order on Local Events BasicDefinitions...122

5 xii Contents A Distributed Execution Is a Partial Order on Local Events Causal Past, Causal Future, Concurrency, Cut Asynchronous Distributed Execution with Respect to Physical Time A Distributed Execution Is a Partial Order on Local States Global State and Lattice of Global States The Concept of a Global State Lattice of Global States Sequential Observations Global States Including Process States and Channel States Global State Including Channel States Consistent Global State Including Channel States Consistent Global State Versus Consistent Cut On-the-Fly Computation of Global States Global State Computation Is an Observation Problem Problem Definition On the Meaning of the Computed Global State Principles of Algorithms Computing a Global State A Global State Algorithm Suited to FIFO Channels PrincipleoftheAlgorithm TheAlgorithm ExampleofanExecution A Global State Algorithm Suited to Non-FIFO Channels TheAlgorithmandItsPrinciples How to Compute the State of the Channels Summary Bibliographic Notes ExercisesandProblems Logical Time in Asynchronous Distributed Systems Linear Time Scalar (or Linear) Time From Partial Order to Total Order: TheNotionofaTimestamp Relating Logical Time and Timestamps with Observations Timestamps in Action: Total Order Broadcast VectorTime Vector Time and Vector Clocks Vector Clock Properties OntheDevelopmentofVectorTime Relating Vector Time and Global States Vector Clocks in Action: On-the-Fly Determination of a Global State Property Vector Clocks in Action: On-the-Fly Determination of the Immediate Predecessors On the Size of Vector Clocks

6 Contents xiii A Lower Bound on the Size of Vector Clocks An Efficient Implementation of Vector Clocks k-restrictedvectorclock MatrixTime Matrix Clock: Definition and Algorithm A Variant of Matrix Time in Action: Discard Old Data Summary Bibliographic Notes ExercisesandProblems Asynchronous Distributed Checkpointing Definitions and Main Theorem Local and Global Checkpoints Z-Dependency, Zigzag Paths, and Z-Cycles The Main Theorem Consistent Checkpointing Abstractions Z-Cycle-Freedom Rollback-Dependency Trackability On Distributed Checkpointing Algorithms Checkpointing Algorithms Ensuring Z-Cycle Prevention An Operational Characterization of Z-Cycle-Freedom A Property of a Particular Dating System Two Simple Algorithms Ensuring Z-Cycle Prevention On the Notion of an Optimal Algorithm forz-cycleprevention Checkpointing Algorithms Ensuring Rollback-Dependency Trackability Rollback-Dependency Trackability (RDT) A Simple Brute Force RDT Checkpointing Algorithm The Fixed Dependency After Send (FDAS) RDT Checkpointing Algorithm Still Reducing the Number of Forced Local Checkpoints Message Logging for Uncoordinated Checkpointing Uncoordinated Checkpointing To Log or Not to Log Messages on Stable Storage ARecoveryAlgorithm AFewImprovements Summary Bibliographic Notes ExercisesandProblems Simulating Synchrony on Top of Asynchronous Systems Synchronous Systems, Asynchronous Systems, and Synchronizers Synchronous Systems Asynchronous Systems and Synchronizers OntheEfficiencySide...222

7 xiv Contents Part III 9.2 Basic Principle for a Synchronizer TheMainProblemtoSolve PrincipleoftheSolutions Basic Synchronizers: α and β Synchronizer α Synchronizer β Advanced Synchronizers: γ and δ Synchronizer γ Synchronizer δ The Case of Networks with Bounded Delays Context and Hypotheses TheProblemtoSolve Synchronizer λ Synchronizer μ When the Local Physical Clocks Drift Summary Bibliographic Notes ExercisesandProblems Mutual Exclusion and Resource Allocation 10 Permission-Based Mutual Exclusion Algorithms TheMutualExclusionProblem Definition ClassesofDistributedMutexAlgorithms A Simple Algorithm Based on Individual Permissions PrincipleoftheAlgorithm TheAlgorithm ProofoftheAlgorithm From Simple Mutex to Mutex on Classes of Operations Adaptive Mutex Algorithms Based on Individual Permissions The Notion of an Adaptive Algorithm A Timestamp-Based Adaptive Algorithm A Bounded Adaptive Algorithm Proof of the Bounded Adaptive Mutex Algorithm AnAlgorithmBasedonArbiterPermissions Permissions Managed by Arbiters PermissionsVersusQuorums QuorumConstruction An Adaptive Mutex Algorithm BasedonArbiterPermissions Summary Bibliographic Notes ExercisesandProblems...274

8 Contents xv 11 Distributed Resource Allocation A Single Resource with Several Instances The k-out-of-m Problem Mutual Exclusion with Multiple Entries: The 1-out-of-M MutexProblem An Algorithm for the k-out-of-m MutexProblem ProofoftheAlgorithm From Mutex Algorithms to k-out-of-m Algorithms Several Resources with a Single Instance Several Resources with a Single Instance Incremental Requests for Single Instance Resources: UsingaTotalOrder Incremental Requests for Single Instance Resources: Reducing Process Waiting Chains Simultaneous Requests for Single Instance Resources andstaticsessions Simultaneous Requests for Single Instance Resources and Dynamic Sessions Several Resources with Multiple Instances Summary Bibliographic Notes ExercisesandProblems Part IV High-Level Communication Abstractions 12 Order Constraints on Message Delivery TheCausalMessageDeliveryAbstraction Definition of Causal Message Delivery A Causality-Based Characterization ofcausalmessagedelivery Causal Order with Respect to Other Message Ordering Constraints A Basic Algorithm for Point-to-Point Causal Message Delivery ASimpleAlgorithm ProofoftheAlgorithm Reduce the Size of Control Information Carried by Messages Causal Broadcast Definition and a Simple Algorithm TheNotionofaCausalBarrier Causal Broadcast with Bounded Lifetime Messages The Total Order Broadcast Abstraction StrongTotalOrderVersusWeakTotalOrder An Algorithm Based on a Coordinator Process oracirculatingtoken...322

9 xvi Contents An Inquiry-Based Algorithm An Algorithm for Synchronous Systems Playing with a Single Channel Four Order Properties on a Channel A General Algorithm Implementing These Properties Summary Bibliographic Notes ExercisesandProblems Rendezvous (Synchronous) Communication The Synchronous Communication Abstraction Definition AnExampleofUse AMessagePattern-BasedCharacterization Types of Algorithms Implementing Synchronous Communications Algorithms for Nondeterministic Planned Interactions Deterministic and Nondeterministic Communication Contexts An Asymmetric (Static) Client Server Implementation AnAsymmetricToken-BasedImplementation An Algorithm for Nondeterministic Forced Interactions Nondeterministic Forced Interactions ASimpleAlgorithm ProofoftheAlgorithm Rendezvous with Deadlines in Synchronous Systems Synchronous Systems and Rendezvous with Deadline Rendezvous with Deadline Between Two Processes Introducing Nondeterministic Choice n-way Rendezvous with Deadline Summary Bibliographic Notes ExercisesandProblems Part V Detection of Properties on Distributed Executions 14 Distributed Termination Detection TheDistributedTerminationDetectionProblem Process and Channel States TerminationPredicate TheTerminationDetectionProblem Types and Structure of Termination Detection Algorithms Termination Detection in the Asynchronous Atomic Model The Atomic Model

10 Contents xvii The Four-Counter Algorithm TheCountingVectorAlgorithm The Four-Counter Algorithm vs.thecountingvectoralgorithm TerminationDetectioninDiffusingComputations TheNotionofaDiffusingComputation A Detection Algorithm Suited to Diffusing Computations A General Termination Detection Algorithm Wave and Sequence of Waves A Reasoned Construction Termination Detection in a Very General Distributed Model Model and Nondeterministic Atomic Receive Statement The Predicate fulfilled() Static vs. Dynamic Termination: Definition DetectionofStaticTermination Detection of Dynamic Termination Summary Bibliographic Notes ExercisesandProblems Distributed Deadlock Detection The Deadlock Detection Problem Wait-ForGraph(WFG) AND and OR Models Associated with Deadlock Deadlock in the AND Model Deadlock in the OR Model The Deadlock Detection Problem Structure of Deadlock Detection Algorithms Deadlock Detection in the One-at-a-Time Model Principle and Local Variables ADetectionAlgorithm ProofoftheAlgorithm Deadlock Detection in the AND Communication Model Model and Principle of the Algorithm ADetectionAlgorithm ProofoftheAlgorithm Deadlock Detection in the OR Communication Model Principle ADetectionAlgorithm ProofoftheAlgorithm Summary Bibliographic Notes ExercisesandProblems...422

11 xviii Contents Part VI Distributed Shared Memory 16 Atomic Consistency (Linearizability) The Concept of a Distributed Shared Memory The Atomicity Consistency Condition WhatIstheIssue? AnExecutionIsaPartialOrderonOperations Atomicity: Formal Definition AtomicObjectsComposeforFree Message-Passing Implementations of Atomicity Atomicity Based on a Total Order Broadcast Abstraction Atomicity of Read/Write Objects Based on ServerProcesses Atomicity Based on a Server Process and Copy Invalidation Introducing the Notion of an Owner Process Atomicity Based on a Server Process and Copy Update Summary Bibliographic Notes ExercisesandProblems Sequential Consistency Sequential Consistency Definition Sequential Consistency Is Not a Local Property Partial Order for Sequential Consistency Two Theorems for Sequentially Consistent Read/Write Registers From Theorems to Algorithms Sequential Consistency from Total Order Broadcast A Fast Read Algorithm for Read/Write Objects A Fast Write Algorithm for Read/Write Objects A Fast Enqueue Algorithm for Queue Objects Sequential Consistency from a Single Server The Single Server Is a Process TheSingleServerIsaNavigatingToken Sequential Consistency with a Server per Object StructuralView The Object Managers Must Cooperate AnAlgorithmBasedontheOOConstraint AWeakerConsistencyCondition:CausalConsistency Definition ASimpleAlgorithm TheCaseofaSingleObject AHierarchyofConsistencyConditions...468

12 Contents xix 17.7Summary Bibliographic Notes ExercisesandProblems Afterword TheAimofThisBook Most Important Concepts, Notions, and Mechanisms PresentedinThisBook HowtoUseThisBook FromFailure-FreeSystemstoFailure-ProneSystems A Series of Books References Index...495

Concurrent Programming: Algorithms, Principles, and Foundations

Concurrent Programming: Algorithms, Principles, and Foundations Algorithms, Principles, and Foundations Bearbeitet von Michel Raynal 1. Auflage 2012. Buch. xxxii, 516 S. Hardcover ISBN 978 3 642 32026