Centralized mutual exclusion

• Problem : What if the coordinator fails?

• Solution : Elect a new one

Leader Election : Problem Statement

• Given is a set of n processes, 1 .. n.• Each process j has variables :

– l.j : true iff j is a leader– up.j : true iff j has not failed

• This is called an auxiliary variable.

• Requirements – In any state, there is at most one non-failed leader

• always (up.j up.k a l.j l.k j = k)

– eventually some process is elected a leader• eventually (exists j :: up.j l.j)

Solving Leader Election via Tree Construction

• You are a leader iff you are a root– Problems?

• In connected (but not fully connected) networks, tree construction and leader election are almost same. – Everyone needs to know how to get to the leader

– The path to leader (often forms a tree)

Algorithms for Leader Election

• There are several algorithms for leader election• We will discuss one of them: Bully Algoirthm

Bully Algorithm

• The goal is to choose the process with highest ID as the leader.

• When a process is repaired or it suspects that the current leader has failed, it starts `election'

• Election process :– [Step 1 :] Make sure that processes with higher ID have failed

– [Step 2 :] If successful, inform all processes with lower ID that a new leader is elected

Bully Algorithm (continued)

• Step 1 – When process j enters the election mode, it sends an

`election' message to j+1, .. n.

– If process k receives the election message from j, it enters the election mode, sends an OK message to j, and sends election message to k+1, n.

– If j receives an OK message, j has lost the election.

– If j does not receive any OK message, j can proceed to step 2.

Bully Algorithm (continued)

• Step 2 :• When process j enters the second step, it has checked that

processes j+1 .. n have failed. It needs to make sure that no process in 1..(j-1) is a leader.

• Process j forces processes (j-1) .. 1 to accept j as the leader.

• Garcia-Molina suggests that this be done using RPC; contact (j-1), (j-2), ..., 1.– This ensures that if two processes `know’ who the leader is then

their information is the same.

Other Approaches

• Probabilistic Algorithm– Each node chooses a random number between [0..N]

– Send the number to all

– Leader = (sum of values received) mod N

– Repeat if this process has failed.

Other Approaches

• Utilize tree construction algorithm– Provides nonmasking fault-tolerance for leader election

• Eventually at most one leader

• Will focus on the idea of diffusing computation that can help ensuring at most one leader at all times