The Strong Diagnosability of Regular Networks and Product Networks under the PMC Model

Strong diagnosability is a more precise concept for measuring the reliability of multiprocessor systems than the traditional global measurement. In this paper, we study the strong diagnosability of multiprocessor systems under the PMC model. Our main objective is to determinate the strong diagnosability of two wide classes of networks, namely regular networks and product networks, subject to certain conditions. Based on our results, we demonstrate the strong diagnosability of several well-known networks, including variants of hypercubes and many others.

[1]  Vinod K. Agarwal,et al.  Diagnosis of t/(t+1)-Diagnosable Systems , 1994, SIAM J. Comput..

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

[3]  Che-Liang Yang,et al.  On Fault Isolation and Identification in t1/t1-Diagnosable Systems , 1986, IEEE Transactions on Computers.

[4]  Lih-Hsing Hsu,et al.  Diagnosability of t-connected networks and product networks under the comparison diagnosis model , 2004, IEEE Transactions on Computers.

[5]  Gerard J. Chang,et al.  (t, k) - Diagnosis for Matching Composition Networks under the MM* Model , 2007, IEEE Transactions on Computers.

[6]  Gerard J. Chang,et al.  (t; k)-Diagnosis for matching composition networks , 2006, IEEE Transactions on Computers.

[7]  GERNOT METZE,et al.  On the Connection Assignment Problem of Diagnosable Systems , 1967, IEEE Trans. Electron. Comput..

[8]  Nian-Feng Tzeng,et al.  Enhanced Hypercubes , 1991, IEEE Trans. Computers.

[9]  Abdel Elah Al-Ayyoub,et al.  The Cross Product of Interconnection Networks , 1997, IEEE Trans. Parallel Distributed Syst..

[10]  Jon T. Butler,et al.  A Characterization of t/s-Diagnosability an Sequential t-Diagnosability in Designs , 1990, IEEE Trans. Computers.

[11]  Arun K. Somani.  Sequential Fault Occurrence and Reconfiguration in System Level Diagnosis , 1990, IEEE Trans. Computers.

[12]  Sabine R. Öhring,et al.  Embeddings Into Hyper Petersen Networks: Yet Another Hypercube-Like Interconnection Topology , 1995 .

[13]  Paul Cull,et al.  The Möbius Cubes , 1995, IEEE Trans. Computers.

[14]  Yuan Yan Tang,et al.  Efficient Fault Identification of Diagnosable Systems under the Comparison Model , 2007, IEEE Transactions on Computers.

[15]  Kyung-Yong Chwa,et al.  On Fault Identification in Diagnosable Systems , 1981, IEEE Transactions on Computers.

[16]  Kozo Kinoshita,et al.  On the Computational Complexity of System Diagnosis , 1978, IEEE Transactions on Computers.

[17]  Yukio Shibata,et al.  (t, k)-Diagnosable System: A Generalization of the PMC Models , 2003, IEEE Trans. Computers.

[18]  Dajin Wang,et al.  Diagnosability of Enhanced Hypercubes , 1994, IEEE Trans. Computers.

[19]  Bih-Sheue Shieh,et al.  On connectivity of the Cartesian product of two graphs , 1999, Appl. Math. Comput..

[20]  Arun K. Somani,et al.  On Diagnosability of Large Fault Sets in Regular Topology-Based Computer Systems , 1996, IEEE Trans. Computers.

[21]  Sanjeev Khanna,et al.  A Graph Partitioning Approach to Sequential Diagnosis , 1997, IEEE Trans. Computers.

[22]  K. H. Kim,et al.  Diagnosabilities of Hypercubes Under the Pessimistic One-Step Diagnosis Strategy , 1991, IEEE Trans. Computers.

[23]  S. Louis Hakimi,et al.  Characterization of Connection Assignment of Diagnosable Systems , 1974, IEEE Transactions on Computers.

[24]  Yukio Shibata,et al.  Diagnosability of Networks Represented by the Cartesian Product (Special Section of Selected Papers from the 12th Workshop on Circuit and Systems in Karuizawa) , 2000 .

[25]  Jimmy J. M. Tan,et al.  Conditional diagnosability measures for large multiprocessor systems , 2005, IEEE Transactions on Computers.

[26]  Peter A. J. Hilbers,et al.  The Twisted Cube , 1987, PARLE.

[27]  M MassonGerald,et al.  On Fault Isolation and Identification in t1/t1-Diagnosable Systems , 1986 .

[28]  GUEY-YUN CHANG,et al.  (t, k)-Diagnosability of Multiprocessor Systems with Applications to Grids and Tori , 2007, SIAM J. Comput..

[29]  Franco P. Preparata,et al.  The cube-connected-cycles: A versatile network for parallel computation , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[30]  Miroslaw Malek,et al.  A comparison connection assignment for diagnosis of multiprocessor systems , 1980, ISCA '80.

[31]  James R. Armstrong,et al.  Fault Diagnosis in a Boolean n Cube Array of Microprocessors , 1981, IEEE Transactions on Computers.

[32]  Sanjeev Khanna,et al.  A Linear Time Algorithm for Sequential Diagnosis in Hypercubes , 1995, J. Parallel Distributed Comput..

[33]  Vinod K. Agarwal,et al.  A Generalized Theory for System Level Diagnosis , 1987, IEEE Transactions on Computers.

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

[35]  Jianxi Fan.  Diagnosability of the Möbius Cubes , 1998, IEEE Trans. Parallel Distributed Syst..

[36]  Gerald M. Masson,et al.  An 0(n2.5) Fault Identification Algorithm for Diagnosable Systems , 1984, IEEE Transactions on Computers.

[37]  David J. Evans,et al.  The locally twisted cubes , 2005, Int. J. Comput. Math..

[38]  Saïd Bettayeb.  On the k-ary Hypercube , 1995, Theor. Comput. Sci..

[39]  Jimmy J. M. Tan,et al.  The diagnosability of the matching composition network under the comparison diagnosis model , 2004, IEEE Transactions on Computers.

[40]  A. Kavianpour,et al.  Sequential diagnosability of star graphs , 1996 .

[41]  Kemal Efe.  A Variation on the Hypercube with Lower Diameter , 1991, IEEE Trans. Computers.

[42]  Abhijit Sengupta,et al.  On Self-Diagnosable Multiprocessor Systems: Diagnosis by the Comparison Approach , 1992, IEEE Trans. Computers.

[43]  Gerard J. Chang,et al.  Diagnosabilities of regular networks , 2005, IEEE Transactions on Parallel and Distributed Systems.