Routing with Quality-of-Service Guarantees: Algorithm and Analysis

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 wK(p)<=WK? • MCOP • Is there an optimal path p from a to d such thatwK(p)<=WK when K = 2? • EMCOP • Is there an optimal path p from a to d such thatwK(p)<=WK when K > 2? AsiaFI 2011

5. Frequently Used Notations • m number of links • n number of nodes • K number of QoS parameters • W1, …, WK K additive constraints • w1, …, wKKQoS metrics on each link • p a path • poptan 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 FullyPolynomial Time Approximation Scheme (FPTAS) and anextended version for QoS routing. • The theoretical analyses show that the proposedalgorithms outperform the previous best-known studies. Andthe numerical results further confirm that FPTAS and itsextended version are effective and efficient for QoSguarantees over different networks. AsiaFI 2011

23. Q&A Thank you! AsiaFI 2011