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Leader election

Leader election . Assumptions Ring topology Synchronous network No failures Goal Exactly one process says: “I am the leader”. Algorithms. Basic Time: O( n ) rounds Message complexity: O( n 2 ) More complicated Time: O( n ) rounds Message complexity: O( n log n ).

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Leader election

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  1. Leader election • Assumptions • Ring topology • Synchronous network • No failures • Goal • Exactly one process says: “I am the leader”

  2. Algorithms • Basic • Time: O(n) rounds • Message complexity: O(n2) • More complicated • Time: O(n) rounds • Message complexity: O(n log n)

  3. Lower bounds - Messages • Comparison based algorithms • O(n log n) messages • In general • O(n) messages • Asynchronous networks • O(n log n)

  4. Shortest path routes • Input • Connected, undirected graph • Destination • Output • Shortest route to destination • Model: self-stabilizing • Asynchronous • Arbitrary failures (corrupt state) • Eventual stabilization

  5. Bellman-Ford • Every so often: • Ask all neighbors distance • Set distance to minimum • Destination always: distance=0 • Stabilizes after n “rounds”

  6. Consensus • Input • 1 or 0 to each node • Output • Agreement: all nodes decide either 0 or 1 • Termination: all nodes eventually decide • Validity: if all inputs 1, then decide 1

  7. Motivation • Many problems equivalent to consensus • Read-Modify-Write Memory • Database commit • Transactional filesystem • Totally ordered broadcast • Distributed firing squad

  8. Universality result • Assume consensus service • Assume non-fault tolerant sequential algorithm (date object) A • Then • There exists a fault-tolerant, wait-free distributed implementation A’ of algorithm A

  9. Asynchronous consensus • Assume 1 stopping failure • Impossible! [FLP 1985] • If consensus algorithm C guarantees agreement and validity • Then • There exists an execution of C that does not terminate

  10. More consensus models • Synchronous • f+1 rounds if f failures • Asynchronous plus eventual synchrony • Eventual synchronized clocks • Eventual message delivery bound d • Consensus terminates • 0((f+4)*d) after stabilization

  11. Failure detectors • Assume total asynchrony • Assume failure detector service • Notifies node i when node j fails • Eventually… • Allow solving consensus • Weakest failure-detector? • Leader-election failure-detector

  12. Byzantine consensus • What if some nodes lie? • Synchronous model • f stopping failures • n nodes • 2f+1 ≤ n

  13. Other consensus problems • Weak consensus • Not feasible • Weak Byzantine consensus • Not feasible • k-set consensus • f < k => feasible • Approximate consensus

  14. Current research • Dynamic networks • Joins/Leaves/Failures • Peer-to-peer networks • Mobile networks • Unknown participants • Large scale networks • Data warehouses • Internet sized applications • Non-blocking, wait-free implementations

  15. Formal methods • IOA language and compiler • Simulator • Proof tools • Larch prover • Daikon invariant detection • Java code generator (in progress)

  16. Summary of results (1)

  17. Summary of results (2)

  18. Models • Nodes • Bounded/unbounded • Unique ids • Known/unknown participants • Communication • Network links • Known/unknown topology • Shared memory

  19. Atomic memory • Definition • Motivation • Algorithms?

  20. FINE Mutual exclusion • Dijkstra • Dining philosophers • Resource allocation

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