Heuristic algorithms for packing of multiple-group multicasting

Multicast communication is an efficient routing method for multimedia data distribution, since it can save network bandwidth during the communication session. Thus, the multicast routing problems have received much attention from many researchers. In this paper, we consider a multicast routing problem with multiple multicast sessions under a capacity limited constraint. This problem is formulated as a tree packing problem. We propose two heuristic algorithms, Steiner-tree-based heuristic (STH) algorithm and cut-set-based heuristic (CSH) algorithm, for solving this problem. The simulation results show that the STH algorithm can find a better approximate solution in a shorter computation time compared to CSH. In addition, if the available bandwidth for the service is just enough, the STH and CSH algorithms may fail to find a solution even if the solution exists. The simulation results also indicate that CSH has a higher probability than STH to find a solution. Thus, it is suggested that one can apply the STH algorithm first to solve the tree packing problem. In case STH fails, CSH algorithm will be used instead.

[1]  Anujan Varma,et al.  Degree-constrained multicasting in point-to-point networks , 1995, Proceedings of INFOCOM'95.

[2]  Weiguo Liu.  A lower bound for the steiner tree problem in directed graphs , 1990, Networks.

[3]  Hans Jürgen Prömel,et al.  The Steiner Tree Problem , 2002 .

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Oktay Günlük,et al.  Optimal packing of group multicastings , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[6]  T. C. Hu,et al.  Multi-Terminal Network Flows , 1961 .

[7]  BERNARD M. WAXMAN,et al.  Routing of multipoint connections , 1988, IEEE J. Sel. Areas Commun..

[8]  Qing Zhu,et al.  A source-based algorithm for delay-constrained minimum-cost multicasting , 1995, Proceedings of INFOCOM'95.

[9]  Chak-Kuen Wong,et al.  A faster approximation algorithm for the Steiner problem in graphs , 1986, Acta Informatica.

[10]  Kang G. Shin,et al.  Localized multicast routing , 1995, Proceedings of GLOBECOM '95.

[11]  S. E. Dreyfus,et al.  The steiner problem in graphs , 1971, Networks.

[12]  Victor J. Rayward-Smith,et al.  On finding steiner vertices , 1986, Networks.

[13]  Pawel Winter,et al.  Steiner problem in networks: A survey , 1987, Networks.

[14]  Sung-Pil Hong,et al.  A fast multicast routing algorithm for delay-sensitive applications , 1997, GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record.

[15]  H. T. Lau.  Steiner Tree Problem , 1986 .

[16]  Rong-Hong Jan,et al.  Optimum multicast of multimedia streams , 1999, Comput. Oper. Res..

[17]  Dana S. Richards,et al.  Steiner tree problems , 1992, Networks.

[18]  John E. Beasley.  An algorithm for the steiner problem in graphs , 1984, Networks.

[19]  Xiaohua Jia,et al.  A group multicast routing algorithm by using multiple minimum Steiner trees , 1997, Comput. Commun..

[20]  Xiaohua Jia,et al.  A distributed algorithm of delay-bounded multicast routing for multimedia applications in wide area networks , 1998, TNET.

[21]  Rolf Floren.  A Note on "A Faster Approximation Algorithm for the Steiner Problem in Graphs" , 1991, Inf. Process. Lett..

[22]  Anantaram Balakrishnan,et al.  Problem reduction methods and a tree generation algorithm for the steiner network problem , 1987, Networks.

[23]  Vorawut Priwan.  The Multicast Tree Based Routing for The Complete Broadcast Multipoint-to-Multipoint Communications , 1995 .

[24]  M. Dror,et al.  Directed Steiner Tree Problem On A Graph: Models, Relaxations And Algorithms , 1990 .

[25]  S. Louis Hakimi,et al.  Steiner's problem in graphs and its implications , 1971, Networks.

[26]  Kurt Mehlhorn,et al.  A Faster Approximation Algorithm for the Steiner Problem in Graphs , 1988, Inf. Process. Lett..

[27]  Richard T. Wong,et al.  A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..