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Advanced QoS Routing Algorithms: Efficient Solutions and Analysis

This paper presents efficient algorithms for Quality of Service (QoS) routing, addressing key challenges due to the NP-hard nature of the problem. We explore the Multi-Constrained Optimal Path (MCOP) and Extra-Multi-Constrained Optimal Path (EMCOP) formulations, providing a fully polynomial-time approximation scheme (FPTAS). Our proposed algorithms outperform existing methods, including an improved binary search technique. We detail their performance through extensive numerics on various network topologies, demonstrating significant efficiency gains in both average running time and weight returned.

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Advanced QoS Routing Algorithms: Efficient Solutions and Analysis

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  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

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