Broadcasting on incomplete hypercubes

Incomplete hypercubes make the hypercubes more flexible on task allocation in large cubes, cost of manufacturing hardware, and hypercubes with faulty nodes. The authors devise and analyze broadcasting algorithms based on the hierarchical binomial spanning trees, hierarchical edge-disjoint spanning trees and edge-disjoint spanning trees in an incomplete hypercube of 2/sup n/+2/sup k/ nodes, where 0<or=k<n. The hierarchical binomial spanning trees have the shortcoming of unbalanced load on parallel paths. In the one-port communication model, in which each node can send message along only one link at a time, the hierarchical edge-disjoint spanning tree algorithms are optimal within a factor of two. The edge-disjoint spanning trees algorithms are optimal with a factor of /sup n+1///sub k+1/ For all-port communication, in which a node can send messages to any number of links adjacent to it, the edge-disjoint spanning trees algorithms are strictly optimal.<<ETX>>

[1]  Jacques Aubert,et al.  Decomposition de la somme cartesienne d'un cycle et de l'union de deux cycles hamiltoniens en cycles hamiltoniens , 1982, Discret. Math..

[2]  Charles L. Seitz,et al.  The cosmic cube , 1985, CACM.

[3]  Marsha F. Foregger Hamiltonian decompositions of products of cycles , 1978, Discret. Math..

[4]  Quentin F. Stout,et al.  Intensive Hypercube Communication. Prearranged Communication in Link-Bound Machines , 1990, J. Parallel Distributed Comput..

[5]  Howard P. Katseff,et al.  Incomplete Hypercubes , 1988, IEEE Trans. Computers.

[6]  Wei-Pang Yang,et al.  Broadcasting on Incomplete Hypercubes , 1993, IEEE Trans. Computers.

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

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

[9]  Ching-Tien Ho,et al.  Optimal communication primitives and graph embeddings on hypercubes , 1990 .

[10]  Wei-Pang Yang,et al.  Hierarchical spanning trees and distributing on incomplete hypercubes , 1991, Parallel Comput..

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

[12]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[13]  Ching-Tien Ho,et al.  Embedding Meshes into Small Boolean Cubes , 1990, Proceedings of the Fifth Distributed Memory Computing Conference, 1990..

[14]  Nian-Feng Tzeng Structural properties of incomplete hypercube computers , 1990, Proceedings.,10th International Conference on Distributed Computing Systems.

[15]  S. Lennart Johnsson,et al.  Distributed Routing Algorithms for Broadcasting and Personalized Communication in Hypercubes , 1986, ICPP.

[16]  M. H. Schultz,et al.  Topological properties of hypercubes , 1988, IEEE Trans. Computers.

[17]  Nian-Feng Tzeng,et al.  Enhanced Incomplete Hypercubes , 1989, ICPP.

[18]  Nian-Feng Tzeng,et al.  Embeddings in Incomplete Hypercubes , 1990, ICPP.