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Lecture 02: Faster Approximations for QoS Routing

Lecture 02: Faster Approximations for QoS Routing. Guoliang (Larry) Xue Department of CSE Arizona State University http://optimization.asu.edu/~xue 13May2008. Outline of the Lecture. Multi-Constrained QoS Routing: OMCP and DCLC Algorithms for MCPP and MCPN

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Lecture 02: Faster Approximations for QoS Routing

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  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.

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