Abstract
We derive a variation of insertion sort that is near optimal with respect to the number of inversions present in the input. The number of comparisons performed by our algorithms, on an input sequence of length n that has I inversions, is at most n log2 ( 1/n +1) + O(n). Moreover, we give an implementation of the algorithm that runs in time O(n log2 ( 1/n +1) + n). All previously known algorithms require at least cn log2( 1/n +1) comparisons for some c > 1.
Supported in part by NSF grant CCR-9732689
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Elmasry, A., Fredman, M.L. (2003). Adaptive Sorting and the Information Theoretic Lower Bound. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_57
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DOI: https://doi.org/10.1007/3-540-36494-3_57
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