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Sorting Real Numbers in \(O\big (n\sqrt{\log n}\big )\) Time and Linear Space

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Abstract

We present an \(O(n\sqrt{\log n})\) time and linear space algorithm for sorting real numbers. This breaks the \(O(n\log n)\) time bound for sorting real numbers which was thought by some researchers to be the lower bound.

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  • 03 December 2019

    The original version of this article unfortunately contained an error in article title and abstract.

References

  1. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)

    MATH  Google Scholar 

  2. Andersson, A.: Faster deterministic sorting and searching in linear space. In: Proceedings of the 1996 IEEE International Conference on Foundations of Computer Science (FOCS’1996), pp. 135–141 (1996)

  3. Andersson, A., Thorup, M.: Tight(er) worest-case bounds on dynamic searching and priority queues. In: Proceedings of the 2000 ACM Symposium on Theory of Computing STOC’2000, pp. 335–342 (2000)

  4. Blum, L., Shub, M., Smale, M.: On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines. In: Proceedings of the 29th IEEE Symposium on Foundations of Computer Science (FOCS’1988), pp. 387–397 (1988)

  5. Corman, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)

    Google Scholar 

  6. Han, Y.: Integer sorting and integer related computation. Proposal submitted to NSF in 2011

  7. Han, Y.: Serial and parallel sorting algorithms with applications. Proposal submitted to NSF in 2012

  8. Han, Y.: Deterministic sorting in \(O(n \log \log n)\) time and linear space. J. Algorithms 50, 96–105 (2004)

    Article  MathSciNet  Google Scholar 

  9. Han, Y.: A linear time algorithm for ordered partition. In: Proceedings of the 2015 International Frontiers in Algorithmic Workshop (FAW’15), LNCS, vol. 9130, pp. 89–103 (2015)

  10. Han, Y., Shen, X.: Conservative algorithms for parallel and sequential integer sorting. In: Proceedings of the 1995 International Conference on Computing and Combinatorics. Lecture Notes in Computer Science, vol. 959, pp. 324–333 (1995, August)

  11. Han, Y., Shen, X.: Parallel integer sorting is more efficient than parallel comparison sorting on exclusive write PRAMs. In: Proceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’99). Baltimore, pp. 419–428, January 1999. Also in SIAM J. Comput. 31(6), 1852–1878 (2002)

  12. Kirkpatrick, D., Reisch, S.: Upper bounds for sorting integers on random access machines. Theor. Comput. Sci. 28, 263–276 (1984)

    Article  MathSciNet  Google Scholar 

  13. Ko, K.: Complexity Theory of Real Functions. Progress in Theoretical Computer Science. Birkhäuser, Boston (1991)

    Book  Google Scholar 

  14. Pǎtraşcu, M., Thorup, M.: Dynamic integer sets with optimal rank, select, and predecessor search. Proceedings of the 2014 IEEE Symposium on Foundations of Computer Science, pp. 166–175 (2014)

  15. Weihrauch, K.: Computable Analysis. Springer, Berlin (2000)

    Book  Google Scholar 

  16. Yap, C.K.: In praise of numerical computation. In: Albers, S., Alt, H., Näher, S. (Eds.) Efficient Algorithms. LNCS, vol. 5760, pp. 380–407

Download references

Acknowledgements

I very much appreciate reviewers’ careful reviewing work that clarified many points in the paper. They made this paper more acceptable to various readers.

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  1. School of Computing and Engineering, University of Missouri at Kansas City, Kansas City, Missouri, 64110, USA

    Yijie Han

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  1. Yijie Han
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Correspondence to Yijie Han.

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The original article has been corrected: The error introduced during conversion process in article title and abstract (symbol Square root has not converted properly) has been corrected in this version.

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Han, Y. Sorting Real Numbers in \(O\big (n\sqrt{\log n}\big )\) Time and Linear Space. Algorithmica 82, 966–978 (2020). https://doi.org/10.1007/s00453-019-00626-0

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