Journal of Information Processing Systems

  • 제7권2호
  • /
  • Pages.271-286
  • /
  • 2011
  • /
  • 1976-913X(pISSN)
  • /
  • 2092-805X(eISSN)
한국정보처리학회 (Korea Information Processing Society)
권호 표지
DOI QR코드

DOI QR Code

Parallel Prefix Computation and Sorting on a Recursive Dual-Net

  • Li, Yamin (Dept. of Computer Science, Hosei University) ;
  • Peng, Shietung (Dept. of Computer Science, Hosei University) ;
  • Chu, Wanming (Dept. of Computer Hardware, University of Aizu)
  • 투고 : 2010.09.27
  • 심사 : 2011.02.13
  • 발행 : 2011.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we propose efficient algorithms for parallel prefix computation and sorting on a recursive dual-net. The recursive dual-net $RDN^k$(B) for k > 0 has $(2n_o)^{2K}/2$ nodes and $d_0$ + k links per node, where $n_0$ and $d_0$ 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 $RDN^k$(B), k > 0, are $2^{k+1}-2+2^kT_{comm}(0)$ and $2^{k+1}-2+2^kT_{comp}(0)$, respectively, where $T_{comm}(0)$ and $T_{comp}(0)$ 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 $RDN^k$(B) is restricted on B = $Q_m$ where $Q_m$ is an m-cube. Assume that each node holds a single data item, the sorting algorithm runs in $O((m2^k)^2)$ computation steps and $O((km2^k)^2)$ communication steps, respectively.

키워드

참고문헌

  1. S. G. Aki, Parallel Computation, Models and Methods, Prentice-Hall, 1997.
  2. F. T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufmann, 1992.
  3. A. Varma and C. S. Raghavendra, Interconnection Networks for Multiprocessors and Multicomputers: Theory and Practice, IEEE Computer Society Press, 1994.
  4. K. Ghose and K. R. Desai, “Hierarchical cubic networks,” IEEE Transactions on Parallel and Distributed Systems, Vol.6, No.4, pp.427–435, April 1995. https://doi.org/10.1109/71.372797
  5. Y. Li and S. Peng, “Dual-cubes: a new interconnection network for high performance computer clusters,” Proceedings of the 2000 International Computer Symposium, Workshop on Computer Architecture, ChiaYi, Taiwan, December 2000, pp.51–57.
  6. Y. Li, S. Peng, and W. Chu, “Efficient collective communications in dual-cube,” The Journal of Supercomputing, Vol.28, No.1, pp.71–90, April 2004. https://doi.org/10.1023/B:SUPE.0000014803.83151.dc
  7. F. P. Preparata and J. Vuillemin, “The cube-connected cycles: a versatile network for parallel computation,” Commun. ACM, Vol.24, pp.300–309, May 1981. https://doi.org/10.1145/358645.358660
  8. Y. Saad and M. H. Schultz, “Topological properties of hypercubes,” IEEE Transactions on Computers, Vol.37, No.7, pp.867–872, July 1988. https://doi.org/10.1109/12.2234
  9. G. H. Chen and D. R. Duh, “Topological properties, communication, and computation on wkrecursive networks,” Networks, Vol.24, No.6, pp.303–317, 1994. https://doi.org/10.1002/net.3230240602
  10. G. Vicchia and C. Sanges, “A recursively scalable network vlsi implementation,” Future Generation Computer Systems, Vol.4, No.3, pp.235–243, 1988. https://doi.org/10.1016/0167-739X(88)90007-6
  11. TOP500, Supercomputer Sites, http://www.top500.org/, Nov. 2010. https://doi.org/10.1016/0167-739X(88)90007-6
  12. P. Beckman, “Looking toward exascale computing, keynote speaker,” in International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT'08), University of Otago, Dunedin, New Zealand, December 2008.
  13. R. Cypher and C. G. Plaxton, “Deterministic sorting in nearly logarithmic time on the hypercube and related computers,” Proceedings of the 22dn Annual ACM Symposium on Theory of Computing, 1990, pp.193–203.
  14. N. R. Adiga, M. A. Blumrich, D. Chen, P. Coteus, A. Gara, M. E. Giampapa, P. Heidelberger, S. Singh, B. D. Steinmacher-Burow, T. Takken, M. Tsao, and P. Vranas, “Blue gene/l torus interconnection network,” IBM Journal of Research and Development, http://www.research.ibm.com/journal/rd/492/tocpdf.html, Vol.49, No.2/3, pp.265–276, 2005. https://doi.org/10.1147/rd.492.0265
  15. Y. Li, S. Peng, and W. Chu, “Recursive dual-net: A new universal network for supercomputers of the next generation,” Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP'09), Taipei, Taiwan, Springer, Lecture Notes in Computer Science (LNCS), June 2009, pp.809–820. https://doi.org/10.1147/rd.492.0265
  16. A. Grama, A. Gupta, G. Karypis, and V. Kumar, Introduction to Parallel Computing, Addison-Wesley, 2003.
  17. W. D. Hillis and G. L. S. Jr, “Data parallel algorithms,” Communications of the ACM, Vol.29, No.12, pp.1170–1183, Dec. 1986. https://doi.org/10.1145/7902.7903
  18. V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to parallel computing: design and analysis of algorithms, Benjamin/Cummings Press, 1994. https://doi.org/10.1145/7902.7903