Implementing HEAPSORT with (n logn - 0.9n) and QUICKSORT with (n logn + 0.2n) comparisons

Authors:
Stefan Edelkamp;Patrick Stiegeler
Affiliations:
Institut für Informatik, Albert-Ludwigs-Universität, Georges-Köhler-Allee, D-79110 Freiburg;Institut für Informatik, Albert-Ludwigs-Universität, Georges-Köhler-Allee, D-79110 Freiburg
Venue:
Journal of Experimental Algorithmics (JEA)
Year:
2002

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Abstract

With refinements to the WEAK-HEAPSORT algorithm we establish the general and practical relevant sequential sorting algorithm INDEX-WEAK-HEAPSORT with exactly n⌈log n⌉ - 2⌈log n⌉ + 1 ≤ n log n-0.9n comparisons and at most n log n + 0.1n transpositions on any given input. It comprises an integer array of size n and is best used to generate an index for the data set. With RELAXED-WEAK-HEAPSORT and GREEDY-WEAK-HEAPSORT we discuss modifications for a smaller set of pending element transpositions.If extra space to create an index is not available, with QUICK-WEAK-HEAPSORT we propose an efficient QUICKSORT variant with n log n + 0.2n + o(n) comparisons on the average. Furthermore, we present data showing that WEAK-HEAPSORT, INDEX-WEAK-HEAPSORT and QUICK-WEAK-HEAPSORT compete with other performant QUICKSORT and HEAPSORT variants.