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# CSL_Talk_20101210

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Brief presentation on the Byzantine agreement problem

Brief presentation on the Byzantine agreement problem

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• 1. Network-Aware Distributed Algorithm
Guanfeng Liang & NitinVaidya
• 2. A Classic Distributed Algorithm Problem
Byzantine Agreement (BA): source S wants to send message to n-1 peers
Fault-free peers must agree
S fault-free agree on its message
Up to f failures
2
• 3. Message Passing Model
3
S
A
C
B
• 4. From a Networking Perspective
Q: What are the link capacities?
A: ∞ bits/second (implicitly)
Q: Is it realistic?
A: ......
4
How does link capacityaffect performance of BA?
• 5. Message Passing with Capacity
Each link has its own fixed capacity
5
S
1
3
1
4
2
2
A
C
1
3
4
2
B
2
5
• 6. Capacity of Agreement
Borrow notions from communications literature
6
Number of bit agreed on [0,t]
t
Throughput = lim
t->∞
Capacity = sup{Throughput}
Send the whole message over each link
Agree on the whole message all at once
Proposed BA alg
Send a fraction of the message over each link using coding
Reach agreement incrementally
Adapts to the location of failures
7
• 8. Data = a, b
S
a
a+b
b
3
1
2
a, b non-binary
Generation 1 - Step 1
8
• 9. Generation 1 - Step 2
Data = a, b
S
a
a+b
b
3
1
b
2
b
a+b
9
a
Data = a, b
S
a
a+b
b
a
b
a+b
a
b’
a+b
3
1
b
2
b’
1 detects error
a
a+b
10
11
S
S
Look the same to 1
a
a
a+b
a+b
b
b’
b
b’
3
3
1
1
2
2
b’
b’
a
a
a+b
a+b
• 12. Generation 1 – Extra Broadcast
a
b
a+b
S
a
b
a+b
a
b’
a+b
3
1
2
12
a
b
a+b
• 13. Generation 1 – Conflict Found
a
b
a+b
S
a
b
a+b
a
b’
a+b
3
1
2
13
a
b
a+b
• 14. Data = c, d
S
c
c+d
d
3
1
2
Generation 2 - Step 1
14
• 15. Generation 2 – Step 2
Data = c, d
S
c
c+d
d
c
d’
c+d
c
c+d
3
1
d’
2
3 detects error
c
c+d
15
• 16. Generation 2 – Extra Broadcast
c
d
c+d
S
c
d’
c+d
c
c+d
3
1
2
16
d’
c+d
• 17. Generation 2 – Failure Identified
c
d
c+d
S
c
d’
c+d
c
c+d
3
1
2
17
d’
c+d
• 18. Improvement over Traditional BA Algorithms
Proposed-> min(2 links) = R + ε
18
S
R
R
ε
3
1
2
• 19. Summary
Capacity of BA given link capacity
Other capacity constraints
Framework for efficient BA
Coding
Incremental agreement
Can be used for multicast with node failure
19
• 20. Thanks you!