1. Distributed Algorithms for Failure Detection in Crash Environments
R. Cortiñas, A. Lafuente, M. Larrea
Distributed Systems Group
University of the Basque Country UPV/EHU

2. Guest Stars: P, S and Omega
P: strong completeness, eventual strong accuracy
Eventually every process that crashes is permanently suspected by every correct process
There is a time after which correct processes are not suspected by any correct process
S: strong completeness, eventual weak accuracy
There is a time after which some correct process is never suspected by any correct process
Omega: eventual leader election
There is a time after which all the correct processes always trust the same correct process
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3. The First P Algorithm [CT96]
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4. Communication Optimality
A ring arrangement of processes
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5. Communication Optimality
Communication-efficient algorithms:
n links are used forever
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6. Communication Optimality
Communication-optimal algorithms:
C links are used forever
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7. Communication-optimal P
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8. Communication-optimal Omega
We also propose an optimal implementation of S, the weakest failure detector for solving Consensus:
processes ordered: p1, ..., pn
heartbeat strategy
communication pattern: one-to-successors
based on a trusted process (instead of a list of suspected processes)
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9. Communication-optimal Omega
i) Initially, p1 starts sending messages periodically to the rest of processes, and all processes trust p1 p1 p2 p3 p4 p5
trusted1 = p1
trusted2 = p1
trusted3 = p1
trusted4 = p1
trusted5 = p1
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10. Communication-optimal Omega
ii) If a process does not receive a message within some timeout period from its trusted process pi, then it suspects pi and takes the next process pi+1 as its new trusted process p1 p2 p3 p4 p5
trusted1 = p1
trusted2 = p1
trusted3 = p1
timeout on p1
trusted4 = p2
trusted5 = p1
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11. Communication-optimal Omega
iii) If a process trusts itself, then it starts sending messages periodically to its successors p1 p2 p3 p4 p5
trusted1 = p1
timeout on p1
trusted2 = p2
trusted3 = p1
trusted4 = p2
trusted5 = p1
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12. Communication-optimal Omega
iv) If a process receives a message from a process pi preceding its trusted process, then it will trust pi again, increasing its timeout period with respect to pi p1 p2 p3 p4 p5
trusted1 = p1
message from p1
trusted2 = p1
timeout_period21++
trusted3 = p2
message from p1
trusted4 = p1
timeout_period41++
trusted5 = p1
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13. Communication-optimal Omega
Lemma. With the previous algorithm, eventually all the correct processes will permanently trust the first correct process in p1, ..., pn
This property trivially allows us to provide the properties of S:
Eventual weak accuracy: by not suspecting the trusted process
Strong completeness: by suspecting all the processes except the trusted process
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14. Communication-optimal Omega
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