On The Average-Case Complexity of Shellsort
نویسندگان
چکیده
We prove a lower bound expressed in the increment sequence on the average-case complexity (number of inversions which is proportional to the running time) of Shellsort. This lower bound is sharp in every case where it could be checked. We obtain new results e.g. determining the average-case complexity precisely in the Yao-Janson-Knuth 3-pass case.
منابع مشابه
ar X iv : c s . C C / 9 90 60 08 v 1 4 J un 1 99 9 Average - Case Complexity of Shellsort
We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω(pn) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.
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We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω(pn 1 p ) for all p ≤ logn. Using similar arguments, we analyze the average-case complexity of several other sorting algorithms.
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We prove a lower bound expressed in the increment sequence on the average-case complexity (number of inversions which is proportional to the running time) of Shellsort. This lower bound is sharp in every case where it could be checked. We obtain new results e.g. determining the average-case complexity precisely in the Yao-Janson-Knuth 3-pass case.
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We show lower bounds on the worst-case complexity of Shellsort. In particular, we give a fairly simple proof of an (n lg 2 n=(lg lg n) 2) lower bound for the size of Shellsort sorting networks, for arbitrary increment sequences. We also show an identical lower bound for the running time of Shellsort algorithms, again for arbitrary increment sequences. Our lower bounds establish an almost tight ...
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Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Dobosiewicz-sort, Shakersort, and sorting with stacks and queues in sequential or parallel mode. Es...
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تاریخ انتشار 2015