Broadcasting in Butterfly and deBruijn Networks

Broadcasting is the process of message dissemination in a communication network in which a message originated by one processor is transmitted to all processors of the network. In this paper, we present a new lower bound of 1.7417m for broadcasting in the butterfly network of dimension m. This improves the best known lower bound of 1.5621m. We also describe an algorithm which improves the upper bound from 2m to 2m−1. This is shown to be optimal for small dimensions m. In addition, the presented lower bound technique is used to derive non-trivial lower bounds for broadcasting in the deBruijn network of dimension m. An upper bound of 1.5m + 1.5 is well-known for this network. Here, we are able to improve the lower bound from 1.1374m to 1.3171m.

[1]  Luisa Gargano,et al.  Time Bound for Broadcasting in Bounded Degree Graphs , 1989, WG.

[2]  Arnold L. Rosenberg,et al.  Group Action Graphs and Parallel Architectures , 1990, SIAM J. Comput..

[3]  Sheldon B. Akers,et al.  A Group-Theoretic Model for Symmetric Interconnection Networks , 1989, IEEE Trans. Computers.

[4]  de Ng Dick Bruijn.  A combinatorial problem , 1946 .

[5]  Dhiraj K. Pradhan,et al.  The De Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI , 1989, IEEE Trans. Computers.

[6]  Ralf Klasing,et al.  Compressing cube-connected cycles and butterfly networks , 1990, Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing 1990.

[7]  Jaroslav Opatrny,et al.  Broadcasting and Spanning Trees in de Bruijn and Kautz Networks , 1992, Discret. Appl. Math..

[8]  Elena Stöhr.  On the Broadcast Time of the Butterfly network , 1991, WG.

[9]  Elena Stöhr.  Broadcasting in the Butterfly Network , 1991, Inf. Process. Lett..

[10]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

[11]  Juraj Hromkovic,et al.  Optimal Algorithms for Dissemination of Information in Some Interconnection Networks (Extended Abstract) , 1990, MFCS.

[12]  Arthur L. Liestman,et al.  Broadcasting in Bounded Degree Graphs , 1992, SIAM J. Discret. Math..

[13]  Burkhard Monien,et al.  Embedding one interconnection network in another , 1990 .

[14]  Arthur L. Liestman,et al.  Broadcast Networks of Bounded Degree , 1988, SIAM J. Discret. Math..

[15]  Marshall C. Pease,et al.  An Adaptation of the Fast Fourier Transform for Parallel Processing , 1968, JACM.

[16]  Pierre Fraigniaud,et al.  Methods and problems of communication in usual networks , 1994, Discret. Appl. Math..