Parallel routing in hypercube networks with faulty nodes

The concept of strong fault-tolerance was introduced to characterize the property of parallel routing. A network G of degree d is said to be strongly fault-tolerant if with at most d-2 faulty nodes, any two nodes u and v in G are connected by min{deg/sub f/(u), deg/sub f/(v)} node-disjoint paths, where deg/sub f/ (u) and deg/sub f/ (v) are the numbers of non-faulty neighbors of the nodes u and v in G, respectively. We show that the hypercube networks are strongly fault-tolerant and develop an algorithm that constructs the maximum number of node-disjoint paths in a hypercube network with faults. Our algorithm is optimal in terms of time and length of node-disjoint paths.

[1]  G. Birkhoff,et al.  A survey of modern algebra , 1942 .

[2]  Ge-Ming Chiu,et al.  A Fault-Tolerant Routing Strategy in Hypercube Multicomputers , 1996, IEEE Trans. Computers.

[3]  J. P. Hayes,et al.  Routing and broadcasting in faulty hypercube computers , 1988, C3P.

[4]  Bella Bose,et al.  All-to-All Broadcasting in Faulty Hypercubes , 1997, IEEE Trans. Computers.

[5]  Shietung Peng,et al.  An Efficient Algorithm for the k-Pairwise Disjoint Paths Problem in Hypercubes , 2000, J. Parallel Distributed Comput..

[6]  Ming-Syan Chen,et al.  Adaptive Fault-Tolerant Routing in Hypercube Multicomputers , 1990, IEEE Trans. Computers.

[7]  Pierre Fraigniaud,et al.  Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers , 1992, IEEE Trans. Computers.

[8]  Shietung Peng,et al.  Optimal Algorithms for Node-to-Node Fault Tolerant Routing in Hypercubes , 1996, Comput. J..

[9]  Jianer Chen,et al.  Strong Fault-Tolerance: Parallel Routing in Star Networks with Faults , 2003, J. Interconnect. Networks.

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

[11]  Shahram Latifi.  Combinatorial Analysis of the Fault-Diameter of the n-cube , 1993, IEEE Trans. Computers.

[12]  Ivan Hal Sudborough,et al.  A topological property of hypercubes: node disjoint paths , 1990, Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing 1990.

[13]  Jianer Chen,et al.  Strong Fault-Tolerance: Parallel Routing in Networks with Faults , 2001, International Conference on Computational Science.

[14]  Chi-Chang Chen,et al.  Nearly Optimal One-to-Many Parallel Routing in Star Networks , 1997, IEEE Trans. Parallel Distributed Syst..

[15]  Khaled Day,et al.  A Comparative Study of Topological Properties of Hypercubes and Star Graphs , 1994, IEEE Trans. Parallel Distributed Syst..

[16]  Garrett Birkhoff,et al.  A survey of modern algebra , 1942 .

[17]  R. M. Thrall.  Review: Garrett Birkhoff and Saunders MacLane, A Survey of Modern Algebra , 1942 .

[18]  Parameswaran Ramanathan,et al.  Reliable Broadcast in Hypercube Multicomputers , 1988, IEEE Trans. Computers.

[19]  M. Krishnamoorthy,et al.  Fault diameter of interconnection networks , 1987 .

[20]  Kang G. Shin,et al.  Interleaved All-to-All Reliable Broadcast on Meshes and Hypercubes , 1994, IEEE Trans. Parallel Distributed Syst..

[21]  P. Hall.  On Representatives of Subsets , 1935 .