Parallel Prefix Computation and Sorting on a Recursive Dual-Net

In this paper, we propose efficient algorithms for parallel prefix computation and sorting on a recursive dual-net. The recursive dual-net (B) for k > 0 has nodes and + k links per node, where and are the number of nod es and the node-degree of the base-network B, respectively. Assume that each node holds one data item, the communication and computation time complexities of the algorithm for parallel prefix computation on (B), k > 0, are and , respectively, where and are the communication and computation time complexities of the algorithm for parallel prefix computation on the base-network B, respectively. The algorithm for parallel sorting on (B) is restricted on B

[1]  Philip Heidelberger,et al.  Blue Gene/L torus interconnection network , 2005, IBM J. Res. Dev..

[2]  W. Daniel Hillis,et al.  Data parallel algorithms , 1986, CACM.

[3]  Frank Thomson Leighton.  Introduction to parallel algorithms and architectures: arrays , 1992 .

[4]  Ian M. Mitchell,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[5]  Shietung Peng,et al.  DUAL-CUBES: A NEW INTERCONNECTION NETWORK FOR HIGH-PERFORMANCE COMPUTER CLUSTERS , 2000 .

[6]  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).

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

[8]  Shietung Peng,et al.  Recursive Dual-Net: A New Universal Network for Supercomputers of the Next Generation , 2009, ICA3PP.

[9]  David Rose,et al.  Topological Properties , 2022 .

[10]  Shietung Peng,et al.  Efficient Collective Communications in Dual-Cube , 2004, The Journal of Supercomputing.

[11]  A. E. Fincham,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[12]  George Karypis,et al.  Introduction to Parallel Computing , 1994 .

[13]  Kanad Ghose,et al.  Hierarchical Cubic Networks , 1995, IEEE Trans. Parallel Distributed Syst..

[14]  D. S. SzyId,et al.  Parallel Computation: Models And Methods , 1998, IEEE Concurrency.

[15]  C. Greg Plaxton,et al.  Deterministic sorting in nearly logarithmic time on the hypercube and related computers , 1990, STOC '90.

[16]  C. Sanges,et al.  A recursively scalable network VLSI implementation , 1988, Future Gener. Comput. Syst..

[17]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[18]  Gen-Huey Chen,et al.  Topological properties, communication, and computation on WK-recursive networks , 1994, Networks.