A Scalable Comparison-Based Diagnosis Algorithm for Hypercube-Like Networks

Comparison-based diagnosis is a realistic approach to detect faults in multiprocessor systems. The Maeng, Malek (MM) model for comparison-based diagnosis defines a strategy based on sending the same input (or task) from a processor to some pair of distinct neighboring processors, and then comparing their responses. Sengupta and Dahbura proposed a further modification of the MM model, called the MM* model, in which any processor v has to test another two processors if v is adjacent to them. Sengupta and Dahbura presented a O(N5)-time diagnosis algorithm for general diagnosable systems under the MM* model, where N is the number of processors in the system. By exploiting the cycle decomposition property, we improve the above result by presenting a O(N(log2N)2)-time diagnosis algorithm for a class of hypercube-like networks under the MM* model.

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

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

[3]  A. Kavianpour,et al.  A comparative evaluation of four basic system-level diagnosis strategies for hypercubes , 1992 .

[4]  A. Ghafoor.  A class of fault-tolerant multiprocessor networks , 1989 .

[5]  A. Ghafoor.  Partitioning of even networks for improved diagnosability (multiprocessor systems) , 1990 .

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

[7]  Abhijit Sengupta,et al.  On self-diagnosable multiprocessor systems: diagnosis by the comparison approach , 1989, [1989] The Nineteenth International Symposium on Fault-Tolerant Computing. Digest of Papers.

[8]  Hyeong-Seok Lim,et al.  Fault-Hamiltonicity of hypercube-like interconnection networks , 2005, 19th IEEE International Parallel and Distributed Processing Symposium.

[9]  Fouad B. Chedid.  On the Generalized Twisted Cube , 1995, Inf. Process. Lett..

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

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

[12]  Fabrizio Lombardi,et al.  Sequential diagnosis of processor array systems , 2004, IEEE Transactions on Reliability.

[13]  Jimmy J. M. Tan,et al.  A Novel Approach to Comparison-Based Diagnosis for Hypercube-Like Systems , 2008 .

[14]  Elias Procópio Duarte,et al.  A survey of comparison-based system-level diagnosis , 2011, CSUR.

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

[16]  Ronald L. Rivest,et al.  Introduction to Algorithms, 3rd Edition , 2009 .

[17]  Takashi Nanya,et al.  A Hierarachical Adaptive Distributed System-Level Diagnosis Algorithm , 1998, IEEE Trans. Computers.

[18]  Jung-Heum Park.  Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m, 4) , 2008, Theor. Comput. Sci..

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

[20]  Krishnan Padmanabhan,et al.  the Twisted Cube Topology for Multiprocessors: A Study in Network Asymmetry , 1991, J. Parallel Distributed Comput..

[21]  Hidekatsu Tokumaru,et al.  Diagnosability and Distinguishability Analysis and Its Applications , 1987, IEEE Transactions on Reliability.

[22]  Kyung-Yong Chwa,et al.  Recursive circulant: a new topology for multicomputer networks (extended abstract) , 1994, Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN).

[23]  Ralph Tindell,et al.  Circulants and their connectivities , 1984, J. Graph Theory.

[24]  P. S. Nagendra Rao,et al.  A class of hypercube-like networks , 1993, Proceedings of 1993 5th IEEE Symposium on Parallel and Distributed Processing.

[25]  David J. Evans,et al.  A comparison-based diagnosis algorithm tailored for crossed cube multiprocessor systems , 2005, Microprocess. Microsystems.

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

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

[28]  Ghafoor.  Partitioning of Even Networks for Improved Diagnosability , 2004 .

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

[30]  Kyung-Yong Chwa,et al.  Schemes for Fault-Tolerant Computing: A Comparison of Modularly Redundant and t-Diagnosable Systems , 1981, Inf. Control..

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

[32]  P. Cull,et al.  The Mobius Cubes , 1991, The Sixth Distributed Memory Computing Conference, 1991. Proceedings.

[33]  Yi Pan.  Fault tolerance in the Block-Shift Network , 2001, IEEE Trans. Reliab..

[34]  Kemal Efe,et al.  The Crossed Cube Architecture for Parallel Computation , 1992, IEEE Trans. Parallel Distributed Syst..

[35]  Xiaola Lin,et al.  The t/k-diagnosability of the BC graphs , 2005, IEEE Transactions on Computers.

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