Abstract
We further simplify Paterson’s version of the Ajtai–Komlós–Szemerédi sorting network, and its analysis, mainly by tuning the invariant to be maintained.
Similar content being viewed by others
References
Ajtai, M., Komlós, J., Szemerédi, E.: Sorting in clog n parallel steps. Combinatorica 3(1), 1–19 (1983)
Ajtai, M., Komlós, J., Szemerédi, E.: An \(\mathcal{O}(n\log n)\) sorting network. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, pp. 1–9. Association for Computing Machinery (1983)
Ajtai, M., Komlós, J., Szemerédi, E.: Halvers and expanders. In: Proceedings, 33rd Annual Symposium on Foundations of Computer Science, pp. 686–692. IEEE Computer Society Press (1992)
Akl, S.G.: Parallel Computation: Models and Methods. Prentice-Hall, Englewood Cliffs (1997)
Alekseev, V.E.: Sorting algorithms with minimum memory. Kibernetika 5(5), 99–103 (September–October, 1969)
Batcher, K.E.: Sorting networks and their applications. In: Spring Joint Computer Conference. AFIPS Conference Proceedings, vol. 32, pp. 307–314. Thompson Book Company (1968)
Chvátal, V.: Lecture notes on the new AKS sorting network. DCS-TR-294, Computer Science Department, Rutgers University (October, 1992)
Cole, R., Ó’Dúnlaing, C.: Note on the AKS sorting network (expository note). Technical Report # 243, Computer Science Department, New York University (1986)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Gibbons, A., Rytter, W.: Efficient Parallel Algorithms. Cambridge University Press, Cambridge (1988)
Knuth, D.E.: The Art of Computer Programming, vol. 3: Sorting and Searching, 2nd edn. Addison-Wesley, Reading (1998)
Manos, H.: Construction of halvers. Inf. Process. Lett. 69(6), 303–307 (1999)
Parberry, I.: Parallel Complexity Theory. Pitman, London (1987)
Paterson, M.S.: Improved sorting networks with \(\mathcal{O}(\log N)\) depth. Algorithmica 5(1), 75–92 (1990)
Pippenger, N.: Communication networks. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, pp. 805–833. Elsevier/MIT Press (1990), Chapter 15
Smith, J.R.: The Design and Analysis of Parallel Algorithms. Oxford University Press, Oxford (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Seiferas, J. Sorting Networks of Logarithmic Depth, Further Simplified. Algorithmica 53, 374–384 (2009). https://doi.org/10.1007/s00453-007-9025-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-007-9025-6