Lecture 02: Faster Approximations for QoS Routing

1
Lecture 02 Faster Approximations for QoS Routing

• Guoliang (Larry) Xue
• Department of CSE
• Arizona State University
• http//optimization.asu.edu/xue
• 13May2008

2
Outline of the Lecture

• Multi-Constrained QoS Routing OMCP and DCLC
• Algorithms for MCPP and MCPN
• Scaling, Rounding, and Approximate Testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• Conclusions

3
Multi-Constrained QoS Routing
4
Multi-Constrained QoS Routing
5
Multi-Constrained QoS Routing
6
Multi-Constrained QoS Routing
7
Multi-Constrained QoS Routing
8
Outline of the Lecture

• Multi-Constrained QoS Routing OMCP and DCLC
• Algorithms for MCPP and MCPN
• Scaling, Rounding, and Approximate Testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• Conclusions

9
MCPP and MCPN
10
Layered Graph
11
Pseudo-Polynomial Time Algorithm for MCPP
12
Pesudopolynomial Time Algorithm for MCPP
13
Pesudopolynomial Time Algorithm for MCPP
14
Pesudopolynomial Time Algorithm for MCPN
15
Pesudopolynomial Time Algorithm for MCPN
16
Pesudopolynomial Time Algorithm for MCPN
17
Outline of the Lecture

• Multi-Constrained QoS Routing OMCP and DCLC
• Algorithms for MCPP and MCPN
• Scaling, Rounding, and Approximate Testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• Conclusions

18
Scaling and Rounding, Approximate Testing (N)
19
Scaling and Rounding, Approximate Testing (N)
20
Scaling and Rounding, Approximate Testing (N)
21
Scaling and Rounding, Approximate Testing (P)
22
Scaling and Rounding, Approximate Testing (P)
23
Scaling and Rounding, Approximate Testing (P)
24
Outline of the Lecture

• Multi-Constrained QoS Routing OMCP and DCLC
• Algorithms for MCPP and MCPN
• Scaling, Rounding, and Approximate Testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• Conclusions

25
The FPTAS of Lorenz and Raz
26
Outline of the Lecture

• Multi-Constrained QoS Routing OMCP and DCLC
• Algorithms for MCPP and MCPN
• Scaling, Rounding, and Approximate Testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• Conclusions

27
The FPTAS of Xue et al.
28
The FPTAS of Xue et al
29
The FTPAS of Xue et al.
30
The FPTAS of Xue et al.
31
The FPTAS of Xue et al.
32
The FPTAS of Xue et al.
33
The FPTAS of Xue et al.
34
The FPTAS of Xue et al.
35
The FPTAS of Xue et al.
36
The FPTAS of Xue et al.
37
Outline of the Lecture

• Multi-Constrained QoS Routing OMCP and DCLC
• Algorithms for MCPP and MCPN
• Scaling, Rounding, and Approximate Testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• Conclusions

38
Conclusions

• We have presented a systematic approach to
  multi-constrained QoS routing. This include
• Pseudo-polynomial time algorithms for MCPP and
  MCPN
• Scaling, rounding, and approximate testing
• The FPTAS of Lorenz and Raz
• The FPTAS of Xue et al.
• It is interesting to see that a faster
  approximation algorithm is obtained by a novel
  combination of two existing techniques.
• This approach has other applications.