Algorithms and Average Time Bounds of Sorting on a Mesh-Connected Computer

IEEE Transactions on Parallel and Distributed Systems

Volumn 5, Issue 3, 1994, Pages 308-315

  Gu, Jun ^b  

^a UNIVERSITY OF AIZU   (Japan)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Average time complexity; mesh connected computer; parallel algorithms; sorting algorithms; torus

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MATHEMATICAL MODELS; MICROPROCESSOR CHIPS; PARALLEL PROCESSING SYSTEMS; PROGRAM PROCESSORS; RANDOM PROCESSES;

AVERAGE TIME COMPLEXITY; MESH CONNECTED COMPUTERS; TORUS;

SORTING;

EID: 0028392989     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/71.277787     Document Type: Article

References (27)

1. M. Ajtai, J. Komlós, and E. Szemerédi, “An o(n log n)sorting network,” Proc. 15th ACM Symp. Theory of Computing, 1983, pp. 1–9.
2. S.G. Akl, Parallel Sorting Algorithms. Orlando, FL: Academic, 1985.
3. D. Angluin and L. Valiant, “Fast probabilistic algorithms for hamiltonian circuits and matchings,” J. Comput. Syst. Sci., vol. 18, pp. 155–193, 1979.
4. G. Bilardi and F. Preparata, “A minimum area VLSI architecture for o(log n) time sorting,” Proc. 16th ACM Symp. Theory of Computing, 1984, pp. 67–70.
5. H. Chernoff, “A measure of asymptotic efficiency for tests of a hypotheses based on the sum of observations,” Ann. Math. Stat., vol. 23, pp. 493–509, 1952.
6. B.S. Chlebus, “Sorting within distance bound on a mesh connected array,” Optimal Algorithm, Lecture Notes Comput. Sci., vol. 401, pp. 232–238, 1989.
7. P. Corbett and I. Scherson, “A unified algorithm for sorting on a multidimensional mesh connected processors,” Infom. Processing. Lett., vol. 37, pp. 225–231, 1991.
8. P. Erdös and I. Spencer, Probabilistic Method in Combinatorics. New York: Academic Press, 1974.
9. Q. P. Gu and A. Maruoka, “Learning monotone Boolean functions by uniformly distributed examples,” SIAM J. Computing, vol. 21, pp. 587–599, June 1992.
10. Q. P. Gu and T. Takaoka, “Time lower bounds for sorting on multidimensional mesh connected processors with wrap around connections,” Tech. Rep. TR-91-2, Dept, of Comput. Sci., Univ. of Ibaraki, Japan, Hitachi, Ibaraki 316, Japan, 1991.
11. Y. Han, Y. Igarashi, and M. Truszczynski, “Indexing functions and time lower bounds for sorting on a mesh connected computer,” Tech. Rep. TR-114-88, Dept, of Comput. Sci., Univ. of Kentucky, 1988.
12. C. Kaklamanis, D. Krizanic, L. Natarayan, and T. Tsantilas, “Randomized sorting and selection on mesh-connected processor arrays,” Proc. Symp. Parall. Algorithms Archetectures, 1991, pp. 17–28.
13. D. E. Knuth, The Art of Computer Programming, vol. 3. Reading, MA: Addison-Wesley, 1973.
14. M. Kumar and D. S. Hirschberg, “An efficient implementation of batcher’s odd-even merge algorithm and its application in parallel sorting schemes,” IEEE Trans. Comp., vol. C-32, pp. 254-264 1983.
15. M. Kunde, “Lower bounds for sorting on mesh connected architectures,” Acta Inform., vol. 24, pp. 121–131, 1987.
16. M. Kunde, “Optimal sorting on multi-dimensionally mesh connected computers,” Proc. 4th Symp. Theoretical Aspects Comput. Lecture Notes in Comput. Sci., vol. 247, 408–419, 1987.
17. M. Kunde, “Concentrated regural data streams on grids: Sorting and routing near to the bisection width,” in Proc. 32nd IEEE Symp. Foundations Comput. Sci., pp. 141–150, 1991.
18. H. W. Lang, M. Schimmler, H. Schmeck, and H. Schroder, “Systolic sorting on a mesh connected network,” IEEE Trans. Comput., vol. C-34, pp. 652–658, 1985.
19. T. Leighton, “Tight bounds on the complexity of parallel sorting,” IEEE Trans. Comput., vol. C-34, pp. 344–354, 1985.
20. T. Leighton, “Tight bounds on the complexity of parallel sorting,” Proc. Symp. Parall. Algorithms and Archetectures, 2–10, 1990.
21. Y. Mansor and L. Schulman, “Sorting on a ring of processors,” J. Algorithm, vol. 11, pp. 622–630, 1990.
22. D. Nassimi and S. Sahni, “Bitonic sort on a mesh connected parallel computer,” IEEE Trans. Comput., vol. C-28, pp. 2–7, 1979.
23. I. Scherson and S. Sen, “Parallel sorting in two dimensional VLSI models of computation,” IEEE Trans. Comput., vol. C-32, pp. 238–249, 1989.
24. C. Schnorr and A. Shamir, “An optimal sorting algorithm for mesh connected computers,” Proc. 18th ACM Symp.Theory Computing, 1986, pp. 263–271.
25. V. Singh, G. Agha, V. Kumar, and C. Tomlinson, “Scalability of parallel sorting on mesh multicomputers,” in Proc. 5th Int. Parall. Processing Symp., 1991.
26. Q. F. Stout, “Mapping vision algorithms to parallel architectures,” Proc. IEEE, special issue on computer vision, 982–995, Aug. 1988.
27. J. D. Ullman, Computational Aspects of VLSI. Rockville, MD: Comput. Sci. Press, 1984.