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YO-YO Leader Election Lijie Wang

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**Using SPIN Used to detect design error in applications;**

descriptions of distributed algorithms.

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**YO-YO Algorithm Minimum finding Consists two parts**

Leader(smallest id node) Consists two parts Preprocessing Iterations

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Basic Components Node Id Neighbors Edge Between nodes Voting through

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**Node Exchange its id with neighbors**

Preprocessing Node Exchange its id with neighbors Edge Direction Small->large (id)

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DAG

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Direction goes down using different ico

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**Local minima ->source ->candidate**

Candidates Local minima ->source ->candidate Preprocessing completed Second part start…

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**Remove candidates Leave the only one**

Iteration Remove candidates Leave the only one Two phases YO- -YO

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**All sink done -> YO- end…**

Source: ⊙->id-> out neighbors Internal: ->all in neighbors-> ⊙->min->out neighbors Sink: ->all in neighbors-> ⊙ All sink done -> YO- end…

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**-YO start… Sink: ⊙->Y ->min; ⊙-> N->others**

Internal: ->all out neighbors-> ⊙ Receive at least one N: ⊙->N-> all in neighbors Receive all Y: ⊙->Y->min; ⊙->N->others Source: all out neighbors -> ⊙

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**Receive at least one N No longer a candidate How?...**

Eliminate candidates Receive all Y Survives (this time) Receive at least one N No longer a candidate How?...

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**Receive at least one N No longer a candidate Become sink or internal**

Reverse N-edge Modify DAG Flip the link with N Receive at least one N No longer a candidate Become sink or internal With reversing Sink and internal not become candidate less candidate

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**Drag down the dead candidates**

And start over…

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YO- [2]

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-YO [2]

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Flip [2]

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**Count the only one candidate Become the leader**

Termination? Count the only one candidate Become the leader To reduce the message To detect termination Only left one source Additional mechanism Pruning

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Pruning Eliminate leaf Eliminate redundant route

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Pruning [1]

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Pruning [2]

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Pruning more [2]

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Pruning [3]

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**Complexity With pruning Without pruning**

Each phase: 2 messages each link Number of phase: log (number of sources) Total: 2*m*log(s) With pruning Though we do not know the exact number of reduced message in each iteration. Surely, the communication cost will be less remarkable Total: 2* 0 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑛𝑘𝑠

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**Thank you For the spin result**

Fail to intall Ispin on the 64-bit system Try to use the Virtual Machine with a 32-bit system Ispin result will be show in the final report Thank you

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