Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

QoS Routing Algorithms Using Fully Polynomial Time Approximation

VIEWS: 9 PAGES: 23

									 Routing with Quality-of-Service
Guarantees: Algorithm and Analysis
          Jun Huang, Xiaohong Huang, Yan Ma
              Beijing Univ. of Posts & Telecom.
                   Agenda
•   Introduction
•   Problem Formulation & Notations
•   Related Work
•   Contributions
•   Main Algorithms and Analysis
•   Numerical result
•   Conclusion

                      AsiaFI 2011
                    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
              Problem Formulation
• MCP
  – Is there a path p from a to d such
    that wK(p)<=WK?
• MCOP                                   (W1, …, WK)                             d
                                                           (w1, …
  – Is there an optimal path p from a                            , wK)
                                                       a
    to d such that wK(p)<=WK when K
                                                                         b
    = 2?
• EMCOP                                                        c             g

  – Is there an optimal path p from a
    to d such that wK(p)<=WK when K                        e
    > 2?



                                   AsiaFI 2011
       Frequently Used Notations
•   m           number of links
•   n           number of nodes
•   K           number of QoS parameters
•   W1, …, WK    K additive constraints
•   w1, …, wK    K QoS metrics on each link
•   p           a path
•   popt        an optimal path
•   epsilon     approximation ratio

                    AsiaFI 2011
                         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
                   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
              Contributions
• A graph-extending dynamic programming
  process in our proposed FPTAS

• Extension for our proposed FPTAS to solve the
  problem of EMCOP




                     AsiaFI 2011
                             ●○○○○○○



  Main Algorithms and Analysis
• MCOP




              AsiaFI 2011
                           ○●○○○○○



Main Algorithms and Analysis




            AsiaFI 2011
   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
                                                           ○○○●○○○



    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
                             ○○○○●○○



  Main Algorithms and Analysis
• EMCOP




              AsiaFI 2011
                                            ○○○○○●○



   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
                                                         ○○○○○○●



    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
                                                                                                                                                                                                      ●○○○○○



                                          Numerical Result
• NSFNet                                                                                                                              8.5
                                                                                                                                          7)
                                                                                                                                                       11
                                                                                                                                                                            .14)                 12
                                                                                                                                 69 ,                         (163.03, 8
                                                                                                                              19.




                                                                                                                                                1)
                                                                                                                         (1




                                                                                                                                            4.5
                                                                                                                   9                                                   11 )
                                                                                                                                                                   , 4.




                                                                                                                                         3,
                                                                                                                                                                41




                                                                                                                                                                                         (100.1
                                                                                                                                                             15.




                                                                                                                                     6.3
                                                                                                                                                        (1




                                                                                                                                                                   (14
                                                                                                                               ( 10
                                                                                0   2)
                                                                           , 5.




                                                                                                                                                                       9



                                                                                                                                                                                     8, 5.9
                                                                                                                                                                        .44
                                                                    5   .25
                                                               ( 22




                                                                                                                    )
                                                                                                                         10




                                                                                                                                                                            ,
                       2




                                                                                                                     3




                                                                                                                                                                           6.6
                                                                                                                  .0




                                                                                                                                                                                            4)
                                              (268.02




                                                                                                              ,5
                                                      ,      6.33)




                                                                                                                                                                               5
                                                                                                              8
                   )




                                                                                                                                                                                )
                                                                                                           .8
               . 95




                                                                                                          7
                                                                                                       (6
                                                                                                  )
               ,6




                                                                                                   6
                                          4                                                            8




                                                                                                .3
                                  3)
          .41




                                                                                             ,5
                            , 3.3




                                                                                                                                                    (1
                        9.97




                                                                                            8
        ( 88




                                              (71


                                                                                                                                                                                13




                                                                                         .4
                     (8




                                                                                                                                                        93
                                                                                       4
                                                                                    (7
                                               .26




                                                                                                                                                          . 77
                           (183.98, 6.0




    1                                                                         4)         6
                                                    ,3




                                                                                                                                                              ,5
                                                                         .0
                                                                    9, 4
                                                      . 74




                                                                                                                                                                  .84
                                                              (74.5




                                                                                                                                                                   )
                                                        )



                                                                                                                                                       7)
                                                                                                                                                  .3
                                                         5                                                                                      ,9
                 )
             .80




                                                                                                                                          .   82
                               5)




                                                                                                                                     25
           ,4




                                                                                                                                (2
                    2
                6.7




                                                                    (1




                                                                                                                                                                                     14
                                                                     61
                     (11




                                                                          .1




                                                                                                                                         5.9                 7)
                                                                             1
                                                                             ,4




                                                                                                                                    .54,
                                                                                                                                (203
                                                                                 .1
                                                                                    5)




                                3             (188.24, 8.0
                                                               5)
                                                                                                7




                                                                              AsiaFI 2011
                                                 ○●○○○○



             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
                            ○○●○○○



        Numerical Result
• ART




              AsiaFI 2011
                            ○○○●○○



        Numerical Result
• ARW




              AsiaFI 2011
                                ○○○○●○



          Numerical Result
• Random networks (ARTRQ)




                  AsiaFI 2011
                                ○○○○○●



          Numerical Result
• Random networks (ARWRQ)




                  AsiaFI 2011
                    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
   Q&A



Thank you!




   AsiaFI 2011

								
To top