Resource placement in three-dimensional tori

In massively parallel processing systems that incorporate hundreds and thousands of processing nodes, the problem of placing a limited number of resources (e.g. printers, disks, software copies, etc.) over processing nodes is of great importance. In this paper, we investigate resource placement in the three-dimensional torus network which is the underlying interconnection network in most current multicomputer. We show that there exists an irregular distance-1 placement only for tori of the form 2x3ix6j,i,[email protected]?N. In addition, we present a new formal proof for the necessary and sufficient conditions for the existence of irregular distance-d placement in 3D tori.

[1]  Bader F. AlBdaiwi,et al.  Perfect Distance-d Placements in 2D Toroidal Networks , 2004, The Journal of Supercomputing.

[2]  Parameswaran Ramanathan,et al.  Resource Placement with Multiple Adjacency Constraints in k-ary n-Cubes , 1995, IEEE Trans. Parallel Distributed Syst..

[3]  Myung M. Bae,et al.  Gray codes for torus and edge disjoint Hamiltonian cycles , 2000, Proceedings 14th International Parallel and Distributed Processing Symposium. IPDPS 2000.

[4]  R. E. Kessler,et al.  Cray T3D: a new dimension for Cray Research , 1993, Digest of Papers. Compcon Spring.

[5]  Bella Bose,et al.  Quasi-perfect resource placements for two-dimensional toroidal networks , 2005, J. Parallel Distributed Comput..

[6]  William J. Dally,et al.  The J-machine Multicomputer: An Architectural Evaluation , 1993, Proceedings of the 20th Annual International Symposium on Computer Architecture.

[7]  Anant Agarwal,et al.  Limits on Interconnection Network Performance , 1991, IEEE Trans. Parallel Distributed Syst..

[8]  Michael D. Noakes,et al.  The J-machine multicomputer: an architectural evaluation , 1993, ISCA '93.

[9]  Yaagoub Ashir,et al.  On Embedding Cycles in k-Ary n-Cubes , 1997, Parallel Process. Lett..

[10]  Myung M. Bae,et al.  Resource placement in torus-based networks , 1996, Proceedings of International Conference on Parallel Processing.

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

[12]  James Sutton,et al.  iWarp: a 100-MOPS, LIW microprocessor for multicomputers , 1991, IEEE Micro.

[13]  Bella Bose,et al.  On resource placements in 3D tori , 2003, J. Parallel Distributed Comput..

[14]  Abdel Elah Al-Ayyoub,et al.  Fault Diameter of k-ary n-cube Networks , 1997, IEEE Trans. Parallel Distributed Syst..

[15]  William J. Dally,et al.  Performance Analysis of k-Ary n-Cube Interconnection Networks , 1987, IEEE Trans. Computers.

[16]  Parameswaran Ramanathan,et al.  Resource Placement in k-Ary n-Cubes , 1992, ICPP.

[17]  Yaagoub Ashir,et al.  Lee Distance and Topological Properties of k-ary n-cubes , 1995, IEEE Trans. Computers.

[18]  Shahram Latifi,et al.  On link-disjoint Hamiltonian cycles of torus networks , 1993, Proceedings of Southeastcon '93.

[19]  Hamid Sarbazi-Azad,et al.  EMPLOYING K-ARY n-CUBES FOR PARALLEL LAGRANGE INTERPOLATION , 2001, Parallel Algorithms Appl..

[20]  Hsing-Lung Chen,et al.  Efficient Resource Placement in Hypercubes Using Multiple-Adjacency Codes , 1994, IEEE Trans. Computers.

[21]  Nian-Feng Tzeng,et al.  Fault-Tolerant Resource Placement in Hypercube Computers , 1991, ICPP.

[22]  Abdel Elah Al-Ayyoub,et al.  Parallel Solution of Dense Linear Systems on the k-Ary n-Cube Networks , 1997, Int. J. High Speed Comput..

[23]  Steve Scott,et al.  Performance of the CRAY T3E Multiprocessor , 1997, SC.