Isomorphic Allocation in k-ary n-cube Systems

Due to its topological generality and flexibility, the k-ary n-cube architecture is actively researched exploring network design tradeoffs as well as characterizing the topology. Processor allocation problem, which has been extensively attempted for hypercubes and meshes, however, has not been addressed for the k-ary n-cube parallel computers. In this paper, we propose Isomorphic Partitioning, where a partitioned subcube retains the high order of dimension of the whole system but with smaller size in each dimension. The partitioned subcubes maintain the advantages of the high order architecture. Extensive simulation reveals the effectiveness of the proposed scheme based on the Isomorphic Partitioning.

[1]  Chita R. Das,et al.  Limit Allocation: An Efficient Processor Management Scheme for Hypercubes , 1994, 1994 Internatonal Conference on Parallel Processing Vol. 2.

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

[3]  D J Evans,et al.  Parallel processing , 1986 .

[4]  Shantanu Dutt,et al.  Are there advantages to high-dimension architectures?: Analysis of k-ary n-cubes for the class of parallel divide-and-conquer algorithms , 1996, ICS '96.

[5]  James R. Goodman,et al.  The Impact of Pipelined Channels on k-ary n-Cube Networks , 1994, IEEE Trans. Parallel Distributed Syst..

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

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

[8]  Chita R. Das,et al.  A Lazy Scheduling Scheme for Hypercube Computers , 1995, J. Parallel Distributed Comput..

[9]  Carmen Carrión,et al.  A flow control mechanism to avoid message deadlock in k-ary n-cube networks , 1997, Proceedings Fourth International Conference on High-Performance Computing.

[10]  Bill Nitzberg,et al.  Noncontiguous Processor Allocation Algorithms for Mesh-Connected Multicomputers , 1997, IEEE Trans. Parallel Distributed Syst..

[11]  Dhabaleswar K. Panda,et al.  Multidestination Message Passing in Wormhole k-ary n-cube Networks with Base Routing Conformed Paths , 1999, IEEE Trans. Parallel Distributed Syst..

[12]  Bella Bose,et al.  Contiguous and Non-Contiguous Processor Allocation Algorithms for kappa-cubes , 1995, ICPP.

[13]  J DallyWilliam,et al.  Performance Analysis of k-ary n-cube Interconnection Networks , 1990 .

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

[15]  Dhiraj K. Pradhan,et al.  Job Scheduling in Mesh Multicomputers , 1994, 1994 Internatonal Conference on Parallel Processing Vol. 2.

[16]  J. Kim,et al.  A Top-Down Processor Allocation Scheme for Hypercube Computers , 1991, IEEE Trans. Parallel Distributed Syst..

[17]  Nian-Feng Tzeng,et al.  A Fast Recognition-Complete Processor Allocation Strategy for Hypercube Computers , 1992, IEEE Trans. Computers.

[18]  William J. Dally,et al.  Deadlock-Free Message Routing in Multiprocessor Interconnection Networks , 1987, IEEE Transactions on Computers.

[19]  Hee Yong Youn,et al.  An Efficient Task Allocation Scheme for 2D Mesh Architectures , 1997, IEEE Trans. Parallel Distributed Syst..

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

[21]  Vipin Chaudhary,et al.  Subcube allocation strategies in a k-ary n-cube , 1993 .

[22]  Chita R. Das,et al.  Processor Management Techniques for Mesh-Connected Multiprocessors , 1995, ICPP.

[23]  Hyunsoo Yoon,et al.  On Submesh Allocation for Mesh Multicomputers: A Best-Fit Allocation and a Virtual Submesh Allocation for Faulty Meshes , 1998, IEEE Trans. Parallel Distributed Syst..

[24]  Ming-Syan Chen,et al.  Processor Allocation in an N-Cube Multiprocessor Using Gray Codes , 1987, IEEE Transactions on Computers.

[25]  John P. Hayes,et al.  Subcube Allocation in Hypercube Computers , 1991, IEEE Trans. Computers.