
A g r e e e m e n t t P r o t t o c o l l s s
1



Processor failures only with synchronous computation
 Crash fault

Omission fault

Malicious fault
Byzantine fault

Synchronous vs. asynchronous computation

A process knows all the messages it expects (synchronous)

Agreement problem is not solvable in an asynchronous system
 We will solve the agreement problem assuming synchronous computation

Clock synchronization

Atomic commit in DDBS
2



An arbitrarily chosen processor (source processor) will broadcast its initial value to all other processors.
 All non-faulty processors agree on the same value

If the source processor is non-faulty, then the common agreed upon value by all non-faulty processors should be the initial value of the source.
 If the source processor is faulty, then all non-faulty processors can agree on any common value
 It is irrelevant what value faulty processors agree on or whether they agree on a value at all.
3


Solution to the Byzantine agreement problem.
 The upper bound on the number of faulty processors.
 In order to reach an agreement on a common value, non-faulty processors need to be free from the influence of faulty processors.
 If faulty processors dominate in number, they can prevent non-faulty processors from reaching a consensus.
 It is impossible to reach a consensus if the number of faulty processors, m, exceeds (n-1)/3.
4


Lamport-Shostak-Pease Algorithm ( OM(m) )
 Requires m+1 rounds of message exchanges.
Assumes fully connected network.
 Solves the Byzantine problem for 3m+1 or more processors in the presence of at most m faulty processors.
5


The recursive algorithm
 Algorithm OM(0).
 The source processor sends its value to every processor.

Each processor uses the value it receives from the source.

Algorithm OM(m), m>0.

The source processor sends its value to every processor.
 For each i, let v i
be the value processor i receives from the source. Processor i acts as the new source and initiates Algorithm OM(m-1) wherein it sends the value v i
to each of the n-2 other processors.
 For each i and each j (!= i), let v j
be the value processor i received from processor j in the above step using Algorithm OM(m-1). Processor i uses the value majority (v
1
, v
2
, v
3
, … , v n-1
).
6


Performance
 O (n m ) message complexity.
 Dolev et al.’s Algorithm
7


 Sites maintain physical clocks that are closely synchronized with one another even in presence of Byzantine failures
 Periodic resynchronization
8


Assumptions:

All clocks are initially synchronized to approximately the same value
 A nonfaulty process’s clocks runs at approximately the correct rate
 A non-faulty process can read the clock value of another non-faulty process with at most a small error.

Clock synchronization algorithm must satisfy:
 At any time, the value of the clocks of all non-faulty processes must be approximately equal

There is a small bound on the amount by which the clock of a non-faulty process is changed during each resynchronization
9


Interactive Convergence Algorithm
 Assumptions:
 Clocks are initially synchronized

Clocks are resynchronized often enough so that two non-faulty clocks never differ by more than

 Each process reads the value of all other processes’ clocks and sets its clock value to the average of these clock values

If a clock value differs from its own clock by more than

, it replaces that value by its own clock value when taking the average
10

 This algorithm brings the clocks of non-faulty processes closer
 Assumptions:
 All processes execute the algorithm instantaneously
 The error in reading another process’ clock is zero
11


Interactive Consistency Algorithm
 Improves the Interactive Convergence Algorithm by:
 Any two processes will compute approximately the same value for a process clock by taking the median of the clock values rather than the mean
 If a process is non-faulty, then every non-faulty process obtains approximately the correct value for this processes clock
 Therefore, if a majority of processes are non-faulty, the median of all the clock values is either approximately equal to a good clock
’s value or it lies between the values of two good clocks
12



Use of the Byzantine agreement protocol in two-phase commit algorithm
13