n-Cube network: node disjoint shortest paths for maximal distance pairs of vertices

In parallel and distributed systems many communications take place concurrently, so the routing algorithm as well as the underlying interconnection network play a vital role in delivering all the messages efficiently. Fault tolerance and performance are often obtained by delivering the messages through node disjoint shortest paths. In this paper we present two efficient algorithms to construct, under certain conditions, pairwise node disjoint shortest paths for pairs of vertices in an n-cube in the presence of faulty nodes. The first algorithm has O(m^2) time complexity, where m is the number of input bits, and the second one takes O(m^3), but it solves more general problem instances. We also present an efficient algorithm for the extreme version of the edge disjoint shortest paths problem when n is odd.

[1]  Ke Qiu,et al.  From Hall's Matching Theorem to Optimal Routing on Hypercubes , 1998, J. Comb. Theory, Ser. B.

[2]  Ellis Horowitz,et al.  Fundamentals of Data Structures , 1984 .

[3]  Teofilo F. Gonzalez,et al.  Complexity of k-Pairwise Disjoint Shortest Paths in the Hypercube and Grid Networks , 2002 .

[4]  Teofilo F. Gonzalez,et al.  Complexity of k-Pairwise Disjoint Shortest Paths in the Undirected Hypercubic Network and Related Problems , 2002, IASTED PDCS.

[5]  Shahram Latifi,et al.  Node-to-Set Vertex Disjoint Paths in Hypercube Networks , 1998 .

[6]  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.

[7]  Richard M. Karp,et al.  On the Computational Complexity of Combinatorial Problems , 1975, Networks.

[8]  Ivan Hal Sudborough,et al.  Disjoint Paths in the Hypercube , 1989, WG.

[9]  O RabinMichael.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989 .

[10]  Y. Shiloach.  The two paths problem is polynomial , 1978 .

[11]  Shietung Peng,et al.  k-Pairwise Cluster Fault Tolerant Routing in Hypercubes , 1997, IEEE Trans. Computers.

[12]  Michael O. Rabin,et al.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989, JACM.

[13]  Shietung Peng,et al.  Node-to-Set and Set-to-Set Cluster Fault Tolerant Routing in Hypercubes , 1998, Parallel Comput..