1. Routing with Quality-of-Service Guarantees: Algorithm and Analysis Jun Huang, Xiaohong Huang, Yan Ma Beijing Univ. of Posts & Telecom.

2. Agenda Introduction Problem Formulation & Notations Related Work Contributions Main Algorithms and Analysis Numerical result Conclusion AsiaFI 2011

3. Introduction The problem of QoS routing is NP-hard Design an efficient QoS routing algorithm is an important open topic Application of QoS routing – Establishing label-switching paths in MPLS – Arranging service-delivering paths in IMS-enabled networks – Constructing wavelength-switching paths in fiber-optics networks AsiaFI 2011

4. Problem Formulation MCP – Is there a path p from a to d such that w K (p)<=W K ? MCOP – Is there an optimal path p from a to d such that w K (p)<=W K when K = 2? EMCOP – Is there an optimal path p from a to d such that w K (p) 2? AsiaFI 2011

5. Frequently Used Notations m number of links n number of nodes K number of QoS parameters W 1, …, W K K additive constraints w 1, …, w K K QoS metrics on each link p a path p opt an optimal path epsilon approximation ratio AsiaFI 2011

6. Related Work MCOP – K=2 – Ergun et al. [1] developed an improved “binary searching” technique to approximate MCOP – The time complexity of Ergun’s method is O(mn/epsilon) which is known as the best result – However, this algorithm is designed for acyclic graph. [1] F. Ergun, R. Sinha, and L. Zhang, “An improved FPTAS for restricted shortest path,” Inf. Process. Lett., vol. 83, no. 5, pp. 287-291, Sept. 2002 AsiaFI 2011

7. Related Work (cont) EMCOP – K>2 – Xue et al. [2] proposed a FPTAS for EMCOP within time O(m(n/epsilon) K-1 ) – However, such FPTAS do not guarantee any constraints to be enforced. – Xue et al. [3] also proposed a FPTAS for EMCOP with time complexity O(mnlog log log n + m(n/epsilon) K-1 ) which guarantees all constraints to be enforced. [2] G. Xue, A. Sen, W. Zhang, J. Tang and K. Thulasiraman, “Finding a path subject to many additive QoS constraints,” IEEE/ACM Trans. Netw., vol. 15, no. 1, pp. 201-211, Feb. 2007. [3] G. Xue, W. Zhang, J. Tang and K. Thulasiraman, “Polynomial time approximation algorithms for multi-constrained QoS routing,” IEEE/ACM Trans. Netw., vol. 16, no. 3, pp. 656-669, Jun. 2008. AsiaFI 2011

8. Contributions A graph-extending dynamic programming process in our proposed FPTAS Extension for our proposed FPTAS to solve the problem of EMCOP AsiaFI 2011

9. Main Algorithms and Analysis MCOP ●○○○○○○ AsiaFI 2011

10. Main Algorithms and Analysis ○●○○○○○ AsiaFI 2011

11. Main Algorithms and Analysis Theorem 1 The worst-case time complexity of proposed FPTAS is Theorem 2 FPTAS finds a (1+  )-approximation for MCOP if ○○●○○○○ Moreover, both of the constraints are enforced. AsiaFI 2011

12. Main Algorithms and Analysis Proposed FTPAS – (1 +  )-approximation with the same time complexity – Designed for a general undirected graph – asymptotically approximate both the cost and delay Ergun’s method – Designed for a specific acyclic graph – minimizes the cost under the delay constraint Conclusion – The proposed FPTAS outperforms Ergun’s method ○○○●○○○ AsiaFI 2011

13. Main Algorithms and Analysis EMCOP ○○○○●○○ AsiaFI 2011

14. Main Algorithms and Analysis Theorem 3 The worst-case time complexity of proposed EFPTAS is Theorem 4 EFPTAS finds a (1+  )-approximation for EMCOP if ○○○○○●○ Moreover, all of the constraints are enforced. AsiaFI 2011

15. Main Algorithms and Analysis EFPTAS – Find a (1 +  )-approximation for EMCOP – Runs much faster than Xue’s algorithm [3] – Find a (1 +  )-approximation with the same complexity with Xue’s algorithm [2] – The constraints of finding path to be enforced Conclusion – Together with the implications of Theorem 1 and Theorem 2, we confirm that our proposed algorithm outperforms the previous best-known algorithms. ○○○○○○● AsiaFI 2011

16. Numerical Result NSFNet ●○○○○○ AsiaFI 2011

17. Numerical Result Performance Metric – Average Running Time (ART) = Total running time for each routing request / Number of runs – Average Returned Weight (ARW) = Total returned weight for each routing request / Number of runs – ARTRQ = Total ART for all routing requests / Number of routing requests – ARWRQ = Total ARW for all routing requests / Number of routing requests ○●○○○○ AsiaFI 2011

18. Numerical Result ART ○○●○○○ AsiaFI 2011

19. Numerical Result ARW ○○○●○○ AsiaFI 2011

20. Numerical Result Random networks (ARTRQ) ○○○○●○ AsiaFI 2011

21. Numerical Result Random networks (ARWRQ) ○○○○○● AsiaFI 2011

22. Conclusion This work addressed QoS routing related problems and proposed a Fully Polynomial Time Approximation Scheme (FPTAS) and an extended version for QoS routing. The theoretical analyses show that the proposed algorithms outperform the previous best-known studies. And the numerical results further confirm that FPTAS and its extended version are effective and efficient for QoS guarantees over different networks. AsiaFI 2011

23. Q&A Thank you! AsiaFI 2011