Abstract
We present a new sorting algorithm which adapts to existing order within the input sequence. Let k be the smallest integer such that a sequence X of length n can be reduced to the empty sequence by the removal of k monotone, increasing or decreasing, subsequences. The algorithm, Slabsort, sorts X in O(n log k) time, without knowing k beforehand, which is optimal in a comparison-based model. In the worst case Slabsort degenerates to a hybrid of Melsort and Exact Quicksort and runs in Θ(n log n) time. Further, k is shown to capture various kinds of existing order proposed in the literature.
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© 1990 Springer-Verlag Berlin Heidelberg
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Levcopoulos, C., Petersson, O. (1990). Sorting shuffled monotone sequences. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_88
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DOI: https://doi.org/10.1007/3-540-52846-6_88
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