On the Heterogeneous Postal Delivery Model for Multicasting

  • Sekharan, Chandra N. (Department of Computer Science, Loyola University of Chicago) ;
  • Banik, Shankar M. (Department of Mathematics and Computer Science) ;
  • Radhakrishnan, Sridhar (School of Computer Science, University of Oklahoma)
  • 투고 : 2010.05.10
  • 심사 : 2011.05.18
  • 발행 : 2011.10.31

초록

The heterogeneous postal delivery model assumes that each intermediate node in the multicasting tree incurs a constant switching time for each message that is sent. We have proposed a new model where we assume a more generalized switching time at intermediate nodes. In our model, a child node v of a parent u has a switching delay vector, where the ith element of the vector indicates the switching delay incurred by u for sending the message to v after sending the message to i-1 other children of u. Given a multicast tree and switching delay vectors at each non-root node 5 in the tree, we provide an O(n$^{\frac{5}{2}}$) optimal algorithm that will decide the order in which the internal (non-leaf) nodes have to send the multicast message to its children in order to minimize the maximum end-to-end delay due to multicasting. We also show an important lower bound result that optimal multicast switching delay problem is as hard as min-max matching problem on weighted bipartite graphs and hence O(n$^{\frac{5}{2}}$) running time is tight.

키워드

참고문헌

  1. L. Kou, G. Markowsky, and L. Berman, "A fast algorithm for steiner trees," Proc. Acta Infonnatica, vol. 14, pp. 145-151, 1981.
  2. S. Ramanathan, "Multicast tree generation in networks with asymmetric links," IEEE/ACM Trans. Netw., vol. 4, no. 4, pp. 573-568, 1996.
  3. H. Takahashi and A. Matsuyama, "An approximate solution for the Steiner problem in graphs," Mathematica Japonica, vol. 24, no. 6, pp. 573-577, 1980.
  4. S. Y. Shi and J. S. Turner, "Multicast routing and bandwidth dimensioning in overlay networks." IEEE J. Sel. Areas Commun., vol. 20, no. 8, pp. 1444-1455, Oct. 2002. https://doi.org/10.1109/JSAC.2002.803065
  5. S. Y. Shi and J. S. Turner, "Routing in overlay networks," in Proc. IEEE INFOCOM, June 2002, pp. 1200-1208.
  6. S. Banerjee, C. Kommareddy, K. Kar, B. Bhattacharjee, and S. Khuller, "Construction of an efficient overlay multicast infrastructure for real-time applications," in Proc. IEEE INFOCOM, Mar. 2003.
  7. A. Riabov, Z. Liu, and L. Zhang, "Overlay multicast trees of minimal delay," in Proc. IEEE ICDCS, 2004.
  8. Y. H. Chu, S. G. Rao, S. Seshan, and H. Zhang, "Enabling conferencing applications on the Internet using an overlay multicast architecture," in Proc. ACM SIGCOMM, Aug. 2001, pp. 55-67.
  9. G. N. Rouskas and l. Baldine, "Multicasting routing with end-to-end delay and delay variations constraints," IEEE J. Sel. Areas Commun., vol. 15, no. 3, pp.346-356,1997. https://doi.org/10.1109/49.564133
  10. S. Kapoor and S. Raghavan, "Improved multicast routing with delay and delay variation constraint," in Proc. IEEE GLOBECOM, 2000, pp. 476-480.
  11. P. Sheu and S. Chen, "A fast and efficient heuristic algorithm for the delay and delay variation bound multicast tree problem," in Proc. Int. Conf. Inf. Netw., Feb. 2001, pp. 611-618.
  12. S. M Banik, S. Radhakrishnan, and C. N. Sekharan, "Multicast routing with delay and delay variation constraints for collaborative applications on overlay networks," IEEE Trans. Parallel Distrib. Syst., vol. 18, no. 3, pp. 421-431, Mar. 2007. https://doi.org/10.1109/TPDS.2007.45
  13. Q. Zhu, M. Parsa, and J. J. Garcia-Luna-Aceves, "A source-based algorithm for delay-constrained minimum-cost multicasting," in Proc. IEEE INFOCOM, Apr. 1995, pp. 377-385.
  14. H. Lee and C. Youn, "Scalable multicast routing algorithm for delay-variation constrained minimum-cost tree," in Proc. IEEE ICC, 2000, pp. 1343-1347.
  15. Y. Bang, S. Radhakrishnan, N. S. V. Rao, and S. G. Batsell, "On multicasting with minimum end-to-end delay," in Proc. Int. Conf. Comput. Commun. Netw., Oct. 1999, pp. 604-609.
  16. F. Bauer and A. Verma, "Degree-constrained multicasting in point-to-point networks," in Proc. Joint Conf. IEEE Comput. Commun. Societies, Apr. 1995.
  17. A. Bar-Noy, S. Guha, J. Naor, and B. Schieber, "Message multicasting in heterogeneous networks," SIAM J. Comput., vol. 30, no. 2, pp. 347-358, 2000. https://doi.org/10.1137/S0097539798347906
  18. E. Brosh, A. Levin, and Y. Shavitt, "Approximation and heuristic algorithms for minimum-delay application-layer multicast trees," IEEE/ACM Trans. Netw., vol. 15, no. 2, pp. 473-484, Apr. 2007. https://doi.org/10.1109/TNET.2007.892840
  19. E. Brosh. "Approximation and heuristic algorithms for minimum delay application-layer multicast trees," Mater's Thesis, Department of EE-Systems, Tel-Aviv University, Israel, 2003.
  20. O. Gross, "The bottleneck assignment problem: An algorithm," in Proc. Rand Symposium on Mathematical Programming, Rand Publications R-351, 1960, pp. 87-88.
  21. E. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rheinhart and Wilson Publishing Company, 1976.
  22. J. E. Hopcroft, and R. M. Karp, "An $n^{\frac{5}{2}}$: algorithm for maximum matchings in bipartite graphs," SIAM J. Comput., vol. 2, pp. 225-231, 1973. https://doi.org/10.1137/0202019
  23. T. Feder and R. Motwani, "Clique partitions, graph compression, and speeding-up algorithms." J. Comput. Syst. Sci., vol. 51, pp. 261-272, 1995. https://doi.org/10.1006/jcss.1995.1065