Abstract
This paper presents the results of using sequential analysis to find increment sequences that minimize the average running time of Shellsort, for array sizes up to several thousand elements. The obtained sequences outperform by about 3% the best ones known so far, and there is a plausible evidence that they are the optimal ones.
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’Aρиστοτέλη: ’Aναλυτиκά, πρτέρα, 64b28-65a37; Σοφιστικοὶ ἔλεγχοι, 181 a 15. In: Aristotelis Opera. Vol. 1: Aristoteles græce, Academia Regia Borussica, Berolini, 1831.
Ghoshdastidar, D., Roy, M. K.: A study on the evaluation of Shell’s sorting technique. Computer Journal 18 (1975), 234–235.
Hibbard, T. N.: An empirical study of minimal storage sorting. Communications of the ACM 6 (1963), 206–213.
Incerpi, J., Sedgewick, R.: Improved upper bounds on Shellsort. Journal of Computer and System Sciences 31 (1985), 210–224.
Janson, S., Knuth, D. E.: Shellsort with three increments. Random Structures and Algorithms 10 (1997), 125–142.
Jiang, T., Li, M., Vitányi, P.: The average-case complexity of Shellsort. Lecture Notes in Computer Science 1644 (1999), 453–462.
Knuth, D.E.: The Art of Computer Programming. Vol. 3: Sorting and Searching. Addison-Wesley, Reading, MA, 1998.
Pratt, V. R.: Shellsort and Sorting Networks. Garland, New York, 1979, PhD thesis, Stanford University, Department of Computer Science, 1971.
Sedgewick, R: A new upper bound for Shellsort. Journal of Algorithms 7 (1986), 159–173.
Sedgewick, R.: Analysis of Shellsort and related algorithms. Lecture Notes in Computer Science 1136 (1996), 1–11.
Shell, D. L.: A high-speed sorting procedure. Communications of the ACM 2 (1959), 30–32.
Tokuda, N: An improved Shellsort. IFIP Transactions A-12 (1992), 449–457.
Wald, A.: Sequential Analysis. J. Wiley & Sons, New York, 1947.
Yao, A. C.: An analysis of (h, k, 1)-Shellsort. Journal of Algorithms 1 (1980), 14–50.
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© 2001 Springer-Verlag Berlin Heidelberg
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Ciura, M. (2001). Best Increments for the Average Case of Shellsort. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_12
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DOI: https://doi.org/10.1007/3-540-44669-9_12
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