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

The Korean Operations Research and Management Science Society (한국경영과학회)
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Point-to-Multipoint Minimum Cost Flow Problem with Convex Cost Function

콘벡스 비용함수를 갖는 점-대-다중점 최소비용 흐름문제

  • Published : 2000.12.01
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Abstract

In this paper, we introduce a point-to-multipoint minimum cost flow problem with convex and demand splitting. A source node transmits the traffic along the tree that includes members of the point-to-multipoint connection. The traffic is replicated by the nodes only at branch points of the tree. In order to minimize the sum of arc costs, we assume that the traffic demand can be splitted and transmitted to destination nodes along different trees. If arc cost is linear, the problem would be a Steiner tree problem in networks eve though demand splitting is permitted. The problem would be applied in transmitting large volume of traffic from a serve to clients in Internet environments. Optimality conditions of the problem are presented in terms of fair tree routing. The proposed algorithm is a finite terminating algorithm for $\varepsilon$-optimal solution. convergence of the algorithm is obtained under monotonic condition and strict convexity of the cost function. Computational experiences are included.

Keywords

References

  1. Network Flows : Theory, Algorithms, and Applications Ahuja, R. K.;T. L. Magnanti;J. B. Orlin
  2. IEEE INFOCOM '93 Routing multipoint connections using virtual paths in an ATM networks Ammar, M. K.;S. Y. Cheung;C. M. Scoglio
  3. Nonlinear programming : Theory and Algorithms Bazaraa, M. S.;H. D. Sherali;C. M. Shetty
  4. Computers and Intractability : A Guide to the Theory of NP-Completeness Garey, M. R.;D. S. Johnson
  5. Routing in the Internet Huitema, C.
  6. Annals of Discrete Mathematics v.53 The Steiner tree problem Hwang, F.K.;D. S. Richards;P. Winter
  7. IEEE INFOCOM '96 An optimal VP-based multicast routing in ATM networks Kim, S. B.
  8. Queueing Systems v.2 Kleinrock, L.
  9. IEEE/ACM Transaction on Networking v.1 no.3 Multicast routing for multimedia communication Kompella, V. P.;J. C. Pasquale;G. C. Polyzos
  10. IP Multicasting Kosiur, D.
  11. IEEE Proc. Commm v.145 no.2 Lower bound for multimedia multicast routing Leung, Y.-W.;B.-T Yang
  12. Mathematical Programming v.24 Iterative methods for variational and complementary problems Pang, J. S.;D. Chan
  13. European Journal of Operational Research v.111 Iterative bundle-based decomposition for large-scale nonseparable convex optimization Park, K.;Y.-S. Shin
  14. IEEE/ACM Transaction on Networking v.6 no.4 An iterative algorithm for delay-constrained minimum-cost multicasting Parsa, M.;Q. Zhu, J. J.;Garcia-Luna-Aceves
  15. IEEE INFOCOM '96 Multicast routing with end-to-end delay and delay variation constraints Rouskas, G. N.;I. Baldine
  16. Telecommunication Networks : Protocols, Modeling and Analysis Schwartz, M.
  17. Math. Japonica v.24 An approximation solution for the Steiner problem in graphs Takahashi, H.;A. Matsuyama
  18. IEEE Journal on Selected Areas in Communications v.6 Routing of Multipoint connections Waxman, B. M.
  19. Networks v.17 Steiner problem in networks : A survey Winter, P.