Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Algorithms for Maximum Integer Multiflow and Multicut in a Ring Network

링 네트워크에서의 최대 다품종정수흐름문제와 최소 다중절단면문제에 대한 해법

  • Published : 2007.06.30
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Abstract

We study the maximum integer multiflow problem and the minimum multicut problem in a ring network. Both problems in a general network are known to be NP-hard. In this paper, we develop polynomial time algorithms to solve the problems. We also prove that even In a ring network, maximum multiflow is not always integral, which implies that the amount of maximum integer flow does not always reach the minimum capacity of multicut.

Keywords

References

  1. 명영수, '정수단위로만 루팅이 허용되는 SONET링의 용량결정문제', 한국경영과학회지, 제25권, 제1호(1998), pp.49-62
  2. 명영수, 김후곤, '분할이 허용된 링의 용량결정문제에 대한 개선된 해법', 한국경영과학지, 제26권, 제4호(2001) pp.99-108
  3. Ahuja, R.K., T.L. Magnanti, and J,B. Orlin, Network Flows: theory, algorithms, and applications, Prentice-Hall, New Jersey, 1993
  4. Bartholdi, J,J., J,B. Orlin, and H.D. Ratliff, 'Cyclic scheduling via integer programs with circular ones,' Operations Research, Vol.28(1980), pp.1074-1085 https://doi.org/10.1287/opre.28.5.1074
  5. Cosares, S., D.N. Deutsch, I. Saniee, and O.J. Wasem, 'SONET toolkit: a decision support system for designing robust and cost-effective fiber-optic networks,' Interfaces, Vol.25(1995), pp.20-40 https://doi.org/10.1287/inte.25.1.20
  6. Cosares, S. and I. Saniee, 'An optimization problem related to balancing loads on SONET rings,' Telecommunication Systems, Vol.3(1994), pp,165-181 https://doi.org/10.1007/BF02110141
  7. Dell'Amico, M.L. and F. Maffioli, 'Exact Solution of the SONET Ring Loading Problem,' Operations Research Letters, Vol.26 (1999), pp,119-129
  8. Frank, A., T. Nishizeki, N. Saito, H. Suzuki, and E. Tardos, 'Algorithms for routing around a rectangle,' Discrete Aplied Mathematics, Vol.40(1992), pp.363-78 https://doi.org/10.1016/0166-218X(92)90007-W
  9. Garey, M.R. and D.S. Johnson, Computers and intractability : a guide to the theory of NP - completeness, W.H. Freeman and Co., New York, 1979
  10. Myung, Y.-S., 'An Efficient Algorithm for the Ring Loading Problem with Integer Demand Splitting,' SIAM J. Discrete Math, Vol.14(2001), pp.291-298 https://doi.org/10.1137/S0895480199358709
  11. Myung, Y.-S., 'Multicommodity flows in cycle graphs,' Discrete Applied Math, Vol.154(2006), pp,1615-1621 https://doi.org/10.1016/j.dam.2006.03.016
  12. Myung, Y.-S. and H.-G. Kim, 'On the Ring Loading Problem with Demand Splitting,' Operations Research Letters, Vol.32(2004) pp,167-173 https://doi.org/10.1016/j.orl.2003.08.001
  13. Myung, Y.-S., H.-G. Kim, and D.-W. Tcha, 'Optimal load balancing on SONET bidirectional rings,' Operations Research, Vol.45 (1997), pp,148-152 https://doi.org/10.1287/opre.45.1.148
  14. Okamura, H. and P.D. Seymour, 'Multicommodity flows in planar graphs,' Journal of Combinatorial Theory Series E, Vol.31(1981), pp.75-81 https://doi.org/10.1016/S0095-8956(81)80012-3
  15. Schrijver. A., Theory of Linear and Integer Programming, Wiley. 1986
  16. Schrijver, A., Combinatorial optimization, Springer-Verlag, Berlin, 2003
  17. Schrijver, A., P. Seymour and P. Winkler, 'The ring loading problem,' SIAM J. Discrete Math, Vol.11(1998) pp.1-14 https://doi.org/10.1137/S0895480195294994
  18. Shyur, C.C., Y.M. Wu, and C.H. Chen, 'A capacity comparison for SONET self-healing ring networks,' IEEE GLOBECOM, Vol.3(1993), pp.1574-1578
  19. Suzuki, H., A. Ishiguro and T. Nishizeki, 'Variable-Priority Queue and Doughnut Routing,' Journal of Algorithm, Vol.13(1992), pp.606-635 https://doi.org/10.1016/0196-6774(92)90059-L
  20. Vachani, R., A. Shulman, and P. Kubat, 'Multicommodity flows in ring networks,' Informs Journal on Computing, Vol.8(1996), pp.235-242 https://doi.org/10.1287/ijoc.8.3.235
  21. Wan, P.-J. and Y. Yang, 'Load-balanced routing in counter rotated SONET rings,' Networks, Vol.35(2000), pp.279-286 https://doi.org/10.1002/1097-0037(200007)35:4<279::AID-NET7>3.0.CO;2-P
  22. Wang, B.-F., 'Linear Time Algorithms for the Ring Loading Problem with Demand Splitting,' Journal of Algorithm, Vol.54(2005) pp.45-57 https://doi.org/10.1016/j.jalgor.2004.03.003
  23. Wu, T.H., Fiber network service survivability, Artech House, Boston, MA, 1992