Abstract
Complexity measures on permutations are defined which can be used to measure presortedness or to prove lower bounds for sorting. We present four functions C, D, E and F s , but concentrate on the function C that was proposed by G. Hotz. The minimum and the average values can be determined, but the maximum value turns out to be difficult to compute. Given a sequence, consider the number of exchanges of two arbitrary elements that are necessary for ordering this sequence; then permutations with maximal C-values seem to describe sequences with a maximal number of such exchanges.
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Bibliography
Knuth, D.E., The Art of Computer Programming, Vol. III: Sorting and Searching, Addison Wesley
Mannila, H., Measures of Presortedness and Optimal Sorting Algorithms, Technical Report 1984/14, Sarja C, University of Helsinki
Hotz, G., private communication, Oberwolfach 1982
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© 1992 B. G. Teubner Verlagsgesellschaft, Leipzig
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Claus, V. (1992). Complexity Measures on Permutations. In: Buchmann, J., Ganzinger, H., Paul, W.J. (eds) Informatik. TEUBNER-TEXTE zur Informatik, vol 1. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-95233-2_6
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DOI: https://doi.org/10.1007/978-3-322-95233-2_6
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-8154-2033-1
Online ISBN: 978-3-322-95233-2
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