One-to-All Broadcasting of Odd Networks for One-Port and All-Port Models

Broadcasting is one of the most important communication primitives used in multiprocessor networks. In this letter, we demonstrate that the broadcasting algorithm proposed by Madabhushi and others is incorrect. We introduce efficient one-to-all broadcasting schemes of even networks for one-port and all-port models. The broadcasting time of the one-port model is 2d-3 and that of the all-port model is d-1. The total time steps taken by the proposed algorithms are optimal.

[1]  Sung-Won Kim,et al.  Comments on "A Class of Fault-Tolerant Multiprocessor Networks" , 2009, IEEE Trans. Reliab..

[2]  S. Lakshmivarahan,et al.  Analysis of the modified even networks , 1991, Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing.

[3]  Arif Ghafoor,et al.  A Study of Odd Graphs as Fault-Tolerant Interconnection Networks , 1991, IEEE Trans. Computers.

[4]  Sung-Won Kim,et al.  Fault Diameter of Even Networks , 2008, 2008 Fourth International Conference on Networked Computing and Advanced Information Management.

[5]  Sung-Won Kim,et al.  Topological Relationships among Folded Hypercubes, Even Graphs and Odd Graphs , 2008, PDPTA.

[6]  Hyeong-Ok Lee,et al.  Comments on "A Study of Odd Graphs as Fault-Tolerant Interconnection Networks" , 2008, IEEE Trans. Computers.

[7]  S. Lennart Johnsson,et al.  Optimum Broadcasting and Personalized Communication in Hypercubes , 1989, IEEE Trans. Computers.

[8]  A. Ghafoor.  A class of fault-tolerant multiprocessor networks , 1989 .

[9]  N. Biggs.  SOME ODD GRAPH THEORY , 1979 .

[10]  Eddie Cheng,et al.  Embedding hypercubes, rings, and odd graphs into hyper-stars , 2009, Int. J. Comput. Math..