Abstract
We present a practically efficient algorithm for the internal sorting problem. Our algorithm works in-place and, on the average, has a running-time of O(n log n) in the length n of the input. More specifically, the algorithm performs n log n + 3n comparisons and n log n + 2.65n element moves on the average.
An experimental comparison of our proposed algorithm with the most efficient variants of Quicksort and Heapsort is carried out and its results are discussed.
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S. Carlsson, A variant of heapsort with almost optimal number of comparisons, Information Processing Letters, Vol. 24, pp. 247–250, 1987.
E.E. Doberkat, An average analysis of Floyd’s algorithm to construct heaps, Information and Control, Vol.61, pp.114–131, 1984.
B. Durian, Quicksort without a stack, Lect. Notes Comp. Sci. Vol. 233, pp.283–289, Proc. of MFCS 1986.
R.W. Floyd, Treesort 3 (alg. 245), Comm. of ACM, Vol. 7, p. 701,1964.
G. Gonnet, R. Baeza-Yates, Handbook of algorithms and data structures, Addison-Wesley, Reading, MA, 1991.
G. Gonnet, J. Munro, Heaps on Heaps, Lect. Notes Comp. Sci. Vol. 140, Proc. of ICALP’82, 1982.
C.A.R. Hoare, Algorithm 63(partition) and algorithm 65(find), Comm. of ACM, Vol. 4(7), pp. 321–322, 1961.
M. Hofri, Analysis of Algorithms: Computational Methods & Mathematical Tools, Oxford University Press, New York, 1995.
J. Katajainen, The Ultimate Heapsort, DIKU Report 96/42, Department of Computer Science, Univ. of Copenhagen, 1996.
J. Katajainen, T. Pasanen, J. Tehuola, Top-down not-up heapsort, Proc. of The Algorithm Day in Copenhagen, Dept. of Comp. Sci., University of Copenhagen, pp. 7–9, 1997.
D.E. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching, Addison-Wesley, 1973.
LEDA, Library of Efficient Data structures and Algorithms, http://www.mpi-sb.mpg.de/LEDA/leda.html.
C.J. McDiarmid, B.A. Reed, Building Heaps Fast, Journal of algorithms, Vol. 10, pp. 352–365, 1989.
B.M.E. Moret, H.D. Shapiro, Algorithms from P to NP, Volume 1: Design and Efficiency, The Benjamin Cummings Publishing Company, 1990.
T. Pasanen, Elementary average case analysis of Floyd’s algorithms to construct heaps, TUCS Technical Report N. 64, 1996.
L. Rosaz, Improving Katajainen’s Ultimate Heapsort, Technical Report N.1115, Laboratoire de Recherche en Informatique, Université de Paris Sud, Orsay, 1997.
R. Sedgewick, Quicksort, Garland Publishing, New York, 1980.
R. Sedgewick, Implementing quicksort programs, Comm. of ACM 21(10) pp.847–857, 1978.
I. Wegener, Bottom-Up-Heapsort, a new variant of Heapsort beating, on an average, Quicksort (if n is not very small), Theorical Comp. Sci., Vol. 118, pp. 81–98, 1993.
I. Wegener, The worst case complexity of McDiarmid and Reed’s variant of Bottom-Up heap sort is less than nlogn+1.1n, Information and Computation, Vol. 97, pp. 86–96, 1992.
J.W. Williams, Heapsort (alg.232), Comm. of ACM, Vol. 7, pp. 347–348, 1964.
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Cantone, D., Cincotti, G. (2000). QuickHeapsort, an Efficient Mix of Classical Sorting Algorithms. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds) Algorithms and Complexity. CIAC 2000. Lecture Notes in Computer Science, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46521-9_13
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DOI: https://doi.org/10.1007/3-540-46521-9_13
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