Transcript Outline of the Talk

Lecture 02: Faster Approximations for QoS Routing
Guoliang (Larry) Xue
Department of CSE
Arizona State University
http://optimization.asu.edu/~xue
13May2008
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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

1
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Multi-Constrained QoS Routing
2
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Multi-Constrained QoS Routing
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Multi-Constrained QoS Routing
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Multi-Constrained QoS Routing
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Multi-Constrained QoS Routing
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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

7
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MCPP and MCPN
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Layered Graph
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Pseudo-Polynomial Time Algorithm for MCPP
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Pesudopolynomial Time Algorithm for MCPP
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Pesudopolynomial Time Algorithm for MCPP
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Pesudopolynomial Time Algorithm for MCPN
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Pesudopolynomial Time Algorithm for MCPN
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Pesudopolynomial Time Algorithm for MCPN
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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

16
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Scaling and Rounding, Approximate Testing (N)
17
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Scaling and Rounding, Approximate Testing (N)
18
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Scaling and Rounding, Approximate Testing (N)
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Scaling and Rounding, Approximate Testing (P)
20
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Scaling and Rounding, Approximate Testing (P)
21
[email protected]
Scaling and Rounding, Approximate Testing (P)
22
[email protected]
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

23
[email protected]
The FPTAS of Lorenz and Raz
24
[email protected]
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
[email protected]
The FPTAS of Xue et al.
26
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The FPTAS of Xue et al
27
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The FTPAS of Xue et al.
28
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The FPTAS of Xue et al.
29
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The FPTAS of Xue et al.
30
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The FPTAS of Xue et al.
31
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The FPTAS of Xue et al.
32
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The FPTAS of Xue et al.
33
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The FPTAS of Xue et al.
34
[email protected]
The FPTAS of Xue et al.
35
[email protected]
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

36
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Conclusions

We have presented a systematic approach to multiconstrained 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.

37
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