Optimal Broadcast in All-Port Wormhole-Routed Hypercubes

We give an optimal algorithm that broadcasts on an n-dimensional hypercube in Theta(n/ log_{2}(n+ 1)) routing steps with wormhole, e-cube routing and all-port communication. Previously, the best algorithm of McKinley and Trefftz requires [n/2] routing steps. We also give routing algorithms that achieve tight time bounds for n leqslant 7.

[1]  Philip K. McKinley,et al.  Efficient Broadcast in All-Port Wormhole-Routed Hypercubes , 1993, 1993 International Conference on Parallel Processing - ICPP'93.

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

[3]  Dennis Gannon,et al.  On the Impact of Communication Complexity on the Design of Parallel Numerical Algorithms , 1984, IEEE Transactions on Computers.

[4]  C. T. Howard Ho,et al.  Optimal Broadcasting on SIMD Hypercubes without Indirect Addressing Capability , 1991, J. Parallel Distributed Comput..

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

[6]  C. T. Howard Ho,et al.  Efficient communication primitives on hypercubes , 1992, Concurr. Pract. Exp..

[7]  Theodore R. Bashkow,et al.  A large scale, homogeneous, fully distributed parallel machine, I , 1977, ISCA '77.

[8]  Ming-Yang Kao,et al.  Efficient Broadcast on Hypercubes with Wormhole and E-Cube Routings , 1995, Parallel Process. Lett..

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

[10]  G. C. Fox,et al.  Solving Problems on Concurrent Processors , 1988 .

[11]  P. K. McKinley,et al.  Efficient collective data distribution in all-port wormhole-routed hypercubes , 1993, Supercomputing '93.

[12]  Lionel M. Ni,et al.  A survey of wormhole routing techniques in direct networks , 1993, Computer.