Throughput optimization …
 Max-flow optimization
 Zongpeng Li’s slides: 2-8 (copies comes next in these slides)
 Network coding
 Butterfly example (in these slides)
 Zongpeng’s slides: 14-15 (copies in these slides)
1
LP: Hello world …
2
LP: Hello world …
3
4
5
Without network coding …
S
T1
T2
 Using unicast, how much can S send to T1 and T2?
Without network coding …
S
 T1 and T2 both
get 50% of
senders capacity
T1
T2
 Using unicast, how much can S send to T1 and T2?
Without network coding …
S
T1
T2
 Using multicast, how much can S send to T1 and T2?
Without network coding …
S
A,B
B
C,D
D
 T1 and T2 both
B
A,B
D
T1
D
C,D
B
get ¾ streams
(75% of senders
capacity)
T2
 Optimization problem equal to “packing of Steiner
trees” (NP-hard problem)
With network coding …
S
A
A
 T1 and T2 both get
2/2 streams (100% of
senders capacity)
 Improvement by 33%
A
B
B
A+B
A+B
T1
B
A+B
T1
S
A,B
B
D
B
D
A,B
D
T1
C,D
S
A
A
C,D
B
A
B
A+B
A+B
T2
B
T1
B
A+B
T1
11
 Savings can also be in
terms of “bandwidth”
…
12
b1
b1
b2
b1
b2
b1
b2
b2
b1
b1
b2
b1
b2
b1
b2
b1+b2
b1+b2
b1+b2
b2
 …or “time” …
14
Network Coding Example (animation)
a b
 A technique to improve:
1. network throughput
2. efficiency
3. scalability
…
a
1
b
a
b
2
3
a
ab
a
b
 Information is coded at
potentially every node
1
2
3
4
5
abb
5
4
b
a
ab
6
Network Coding Example (without)
a b
 A technique to improve:
1. network throughput
2. efficiency
3. scalability
…
a
1
b
a
2
b
3
a
b a
 Information is coded at
potentially every node
1
2
3
4
5
b
5
4
b
a
6
Network Coding Example (with)
a b
 A technique to improve:
1. network throughput
2. efficiency
3. scalability
…
a
1
b
a
b
2
3
a
ab
a
b
 Information is coded at
potentially every node
1
2
3
4
ab
5
4
b
ab
6
18
19
20