Efficient fault-tolerant routing algorithm for OTIS-cube using unsafety vectors

For the first time this paper proposes a new fault-tolerant routing algorithm for the well known class of network, OTIS-cube. In this new proposed algorithm, each node A starts by computing the first level unsafety set, SA1, composed of the set of unreachable direct neighbours. It then performs m-1 exchanges with its neighbours to determine the k-level unsafety sets SAk for all 1 ≤ k ≤ m, where m is an adjustable parameter between 1 and 2n+1. Equipped with these unsafety sets we show how each node calculates numeric unsafety vectors and uses them to achieve efficient fault-tolerant routing. The paper presents also a performance analysis through extensive simulation experiments proving the superiority of the proposed algorithm using the set of unsafety vectors by showing how the destination is reached by using these sets of unsafety vectors. The simulation results are obtained in terms of routing distances and percentage of reachability.

[1]  S.W. Graham,et al.  The Cost of Broadcasting on Star Graphs and k-Ary Hypercubes , 1993, IEEE Trans. Computers.

[2]  Mohamed Ould-Khaoua,et al.  Unsafety vectors: a new fault-tolerant routing for the binary n-cube , 2002, J. Syst. Archit..

[3]  S C Esener,et al.  Optical transpose interconnection system architectures. , 1993, Optics letters.

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[5]  Sartaj Sahni,et al.  BPC Permutations on the OTIS-Hypercube Optoelectronic Computer , 1998, Informatica.

[6]  Sanjay Ranka,et al.  Embedding meshes on the star graph , 1990, Proceedings SUPERCOMPUTING '90.

[7]  Sartaj Sahni,et al.  Basic Operations on the OTIS-Mesh Optoelectronic Computer , 1998, IEEE Trans. Parallel Distributed Syst..

[8]  John P. Hayes,et al.  A Fault-Tolerant Communication Scheme for Hypercube Computers , 1992, IEEE Trans. Computers.

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

[10]  Daniel H. Linder,et al.  An Adaptive and Fault Tolerant Wormhole Routing Strategy for k-Ary n-Cubes , 1994, IEEE Trans. Computers.

[11]  Justin R. Rattner.  Concurrent processing: a new direction in scientific computing in afips conference proceedings , 1985 .

[12]  Yousef Saad,et al.  Data Communication in Hypercubes , 1989, J. Parallel Distributed Comput..

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

[14]  Quentin F. Stout,et al.  Hypercube message routing in the presence of faults , 1988, C3P.

[15]  Sheldon B. Akers,et al.  The Star Graph: An Attractive Alternative to the n-Cube , 1994, ICPP.

[16]  Karen A. Loveland,et al.  LARGE SCALE , 1991 .

[17]  Ramamohan Paturi,et al.  Scalable Network Architectures Using the Optical Transpose Interconnection System (OTIS) , 2000, J. Parallel Distributed Comput..

[18]  Sartaj Sahni,et al.  Algorithms for the otis optoelectronic computer , 1998 .

[19]  Khaled Day,et al.  Arrangement Graphs: A Class of Generalized Star Graphs , 1992, Inf. Process. Lett..

[20]  T GaughanPatrick,et al.  Adaptive routing protocols for hypercube interconnection networks , 1993 .

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

[22]  Ming-Syan Chen,et al.  Depth-First Search Approach for Fault-Tolerant Routing in Hypercube , 1990, IEEE Trans. Parallel Distributed Syst..

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

[24]  Youran Lan.  A Fault-Tolerant Routing Algorithm in Hypercubes , 1994, ICPP.

[25]  Abdel Elah Al-Ayyoub,et al.  Topological Properties of OTIS-Networks , 2002, IEEE Trans. Parallel Distributed Syst..

[26]  Sartaj Sahni,et al.  BPC permutations on the OTIS-Mesh optoelectronic computer , 1997, Proceedings of the Fourth International Conference on Massively Parallel Processing Using Optical Interconnections.

[27]  P. Marchand,et al.  Grain-size considerations for optoelectronic multistage interconnection networks. , 1992, Applied optics.