2.2分布式算法(2)-领导者选举

Often, there is no owner or master that is automatically considered as coordinator


选举问题

Many distributed systems are client server based, with one server/coordinator (leader), and multiple clients
What happens if the leader fails?


Elect a new one

Cannot assume only one process detects the crash

The election should get all of the processes to agree that one node is a leader

Max identity and Min identity available (extreme values)
Remark



Processors are in one of three states: undecided, leader, lost Initially every process is in the undecided state When leaving the undecided state, a processor goes into a terminated state (leader or lost)
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
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Initially only know myself
Send my id, and wait Repeat forwarding and collecting ids until we receive our id Termination: did we win or lose
Non-initiators just forward and lose
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initiator
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)



Let every initiator send a token with their identity around the whole ring Nodes are not allowed to initiate after they receive a token (example…)
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
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initiator
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
Fra Baidu bibliotek么是选举
“to start from a configuration where all processes are in the same state and arrive at a configuration where exactly one process is the leader”
Goal: to obtain low message complexity
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initiator
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initiator
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
分布协同计算基础
第二章:
分布式算法(2) ---领导者选举
张锡哲 副教授 计算机应用技术研究所 东北大学信息科学与工程学院
选举问题

If we are using one process as a coordinator for a shared resource … …how do we select that one process?


when a centralized algorithm is to be executed in a distributed system for instance, after a system crash when it is unknown which nodes are working
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
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not allowed to initiate

Fully asynchronous system

No global clock, transmission times arbitrary

Every process has a unique identity

Identities are totally ordered Because we have finite number of processes:
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LeLann’s ring election
Message Complexity

Worst case is every node is initiator (N)

Every initiator sends N messages

Gives a total of N2 messages
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时间复杂度

Assume last initiator f starts at time N-1

It reaches a terminal configuration, and in each reachable terminal configuration one process is in state leader and the rest are in the state lost
假设
选举谁？

Basic idea:

If each process has a unique identity, and the identities are ordered

Elect the non-crashed node with minimum/maximum identity
选举算法的应用



When a node receives a token with larger id than itself, why should it keep forwarding it? It is a waste, we know that that id will never win! Lets drop tokens with larger ids than ourselves!

Whenever a node receives back its id, it has seen every other initiators id

Assuming FIFO channels

Let every node keep a list of every identifier seen (listp)

If node s token is dropped, it will anyway receive another token with lower id

In that case, s should set state=lost
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Chang and Roberts Algo
Initiator sends its token While not leader, keep receiving tokens Otherwise, only forward if it’s lower id than me and lose
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
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8 2 5
9 6
3
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initiator
not allowed to initiate
initiator
not allowed to initiate
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Example

Nodes are not allowed to initiate a message after they receive a token (example…)
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not allowed to initiate
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How to make it work


But if we drop a token with id s, node s will be waiting forever on its token to come back How do we solve that?
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How to make it work

If non-initiator, state=lost immediately If initiator, when own id received:
state=leader if min{listp}=p state=lost otherwise

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LeLann’s Algorithm

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f terminates after its token has circulated the ring, N steps
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initiator

Time complexity 2N-1
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Chang-Roberts 算法


Chang and Roberts came up with a small improvement Idea:
环网上的选举
单向环 双向环
LeLann 77, O(N2) Chang-Roberts 79 Ω(N2), Θ(NlogN) Hirshberg et al. 80 Ω(NlogN) Petersen/Dolev et al. 82 Ω(NlogN)
环网上的选举

The first ever election algorithm was done for rings by LeLann Simple idea:
选举算法的定义

Formally, an algorithm is an election algorithm iff:

Each process has the same local algorithm The algorithm is decentralized

It can be initiated by any number of processes in the system