
QuickMergesort: Practically Efficient ConstantFactor Optimal Sorting
We consider the fundamental problem of internally sorting a sequence of ...
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Pivot Sampling in QuickXSort: Precise Analysis of QuickMergesort and QuickHeapsort
QuickXSort is a strategy to combine Quicksort with another sorting metho...
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On the Average Case of MergeInsertion
MergeInsertion, also known as the FordJohnson algorithm, is a sorting a...
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Huskysort
Much of the copious literature on the subject of sorting has concentrate...
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Engineering Inplace (Sharedmemory) Sorting Algorithms
We present sorting algorithms that represent the fastest known technique...
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Sorting by Swaps with Noisy Comparisons
We study sorting of permutations by random swaps if each comparison give...
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Generalized Sorting with Predictions
Generalized sorting problem, also known as sorting with forbidden compar...
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QuickXsort  A Fast Sorting Scheme in Theory and Practice
QuickXsort is a highly efficient inplace sequential sorting scheme that mixes Hoare's Quicksort algorithm with X, where X can be chosen from a wider range of other known sorting algorithms, like Heapsort, Insertionsort and Mergesort. Its major advantage is that QuickXsort can be inplace even if X is not. In this work we provide general transfer theorems expressing the number of comparisons of QuickXsort in terms of the number of comparisons of X. More specifically, if pivots are chosen as medians of (not too fast) growing size samples, the average number of comparisons of QuickXsort and X differ only by o(n)terms. For medianofk pivot selection for some constant k, the difference is a linear term whose coefficient we compute precisely. For instance, medianofthree QuickMergesort uses at most n n  0.8358n + O( n) comparisons. Furthermore, we examine the possibility of sorting base cases with some other algorithm using even less comparisons. By doing so the averagecase number of comparisons can be reduced down to n n 1.4106n + o(n) for a remaining gap of only 0.0321n comparisons to the known lower bound (while using only O( n) additional space and O(n n) time overall). Implementations of these sorting strategies show that the algorithms challenge wellestablished library implementations like Musser's Introsort.
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