LASOB 상에서 계산 트리 형식을 생성하기 위한 최적 병렬 알고리즘

An Optimal Parallel Algorithm for Generating Computation Tree Form on Linear Array with Slotted Optical Buses

  • 김영학 (금오공과대학교 컴퓨터공학부)
  • 발행 : 2000.05.15

초록

최근에 전자 버스 대신에 광 버스를 사용하여 버스의 대역폭을 늘리고 하드웨어의 복잡도를 줄이기 위한 처리기 배열의 구조가 다수의 문헌에서 제안되었다. 본 논문에서는 먼저 슬롯된 광 버스를 갖는 선형 처리기 배열(LASOB) 상에서 괄호 매칭 문제에 대한 상수 시간 알고리즘을 제안한다. 다음에 이 알고리즘을 사용하여 길이 n의 대수 식이 주어지면 n개의 처리기를 갖는 LASOB 상에서 상수 시간에 계산 트리 형식을 생성하는 비용이 최적인 병렬 알고리즘을 제안한다. 아직 임의의 병렬 컴퓨터 모델에서 이 문제에 대한 상수 시간에 수행되는 비용 최적인 병렬 알고리즘은 알려지지 않고 있다.

Recently, processor arrays to enhance the banRecently, processor arrays to enhance the bandwidth of buses and to reduce the complexity of hardwares, using optical buses instead of electronic buses, have been proposed in manyliteratures. In this paper, we first propose a constant-time algorithm for parentheses matching problemon a linear array with slotted optical buses (LASOB).Then, given an algebraic expression of length n, we also propose a cost optimal parallel algorithmthat constructs computational tree form in the steps of constant time on LASOB with n processorsby using parentheses matching algorithm. A cost optimal parallel algorithm for this problem that runsin constant time has not yet been known on any parallel computation models.

키워드

참고문헌

  1. M. Hamdi, C. Qiao, Y. Pan, and J. Tong, 'Communication-efficient sorting algorithms on reconfigurable array of processors with slotted optical buses,' J. Parallel Distribut. Comput. 57, pp. 166-187, 1999 https://doi.org/10.1006/jpdc.1998.1525
  2. S. Pavel and S. G. Akl, 'On the power of arrays with reconfigurable optical buses,' Proc. Int'l Conf. Parallel and Distributed Processing Techniques and Applications, vol. III, 1443-1454, 1996
  3. S. Pavel and S. G. Akl, 'Integer sorting and routing in arrays with reconfigurable optical buses,' Proc. Int'l Conf. on Parallel Processing, vol. II, pp. 90-94, 1996 https://doi.org/10.1109/ICPP.1996.537386
  4. Z. Guo, 'Sorting on array processors with pipelined buses,' Proc. Int'l Conf. on Parallel Processing, vol. III, pp. 289-292, 1992
  5. S. Rajsekaran and S. Sahni, 'Sorting, selection and routing on the array with reconfigurable optical buses,' Technical Report, Department of Computer and Information Science, University of Florida, 1996
  6. R. Miller, V. K. Prasanna-Kumar, D. Reisis, and Q. F. Stout, 'Parallel computations on reconfigurable meshes,' IEEE Trans. Comput., vol. 42, no. 6, pp. 678-692, Jun. 1994 https://doi.org/10.1109/12.277290
  7. H. M. Alnuweiri, 'Parallel constant-time connectivity algorithms on a reconfigurable network of processors,' IEEE Trans. Parallel Distribut. Systems, vol. 6, no. 1, pp. 105-110, Jan. 1995 https://doi.org/10.1109/71.363405
  8. E. Dekel and S. Sahni, 'Parallel generation of postfix and tree forms,' ACM Trans. Programming Languages and Systems 5, pp. 300-317, 1983 https://doi.org/10.1145/2166.357211
  9. I. Bar-On and U. Vishkin, 'Optimal parallel generation of a computation tree form,' ACM Trans. Programming Languages and Systems 7, pp. 384-357, 1985 https://doi.org/10.1145/3318.3478
  10. W. W. Tsang, T. W. Lam, and F. Y. L. Chin, 'An optimal EREW parallel algorithm for parenthesis matching,' Proc. Int'l Conf. on Parallel Processing, vol. III, pp. 185-192, 1989
  11. G. H. Chen, S. Olariu, J. L. Schwing, B. F. Wang, and J. Zhang, 'Constant-time tree algorithms on reconfigurable meshes on size $n{\times}n$,' J. Parallel Distribut. Comput. 26, pp. 137-150, 1995 https://doi.org/10.1006/jpdc.1995.1055
  12. S. G. Akl, The design and analysis of parallel algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1989
  13. L. Bergogne and C. Cerin, 'A new parallel algorithm for the parentheses matching problem,' Proc. AIZU Int'l Symposium on Parallel Algorithms/Architecture Synthesis, pp. 364-369, 1997 https://doi.org/10.1109/AISPAS.1997.581700
  14. K. Diks and W. Rytter, 'On optimal parallel computations for sequence of brackets, ' Theoretical Computer Science, vol 87, pp. 251-262, Sep. 1991 https://doi.org/10.1016/0304-3975(91)90326-W
  15. I. Stojmenovic, 'Constant time BSR solutions to parenthesis matching, tree decoding and tree reconstruction from its traversals,' IEEE Trans. Parallel Distribut. Systems, vol. 7, no. 2, pp. 216-224 , Feb. 1996 https://doi.org/10.1109/71.485530
  16. D. E. Knuth, The art of computer programming: Fundamental algorithms, Addison-Wesley, Reading, MA, 1973