
QuickXsort  A Fast Sorting Scheme in Theory and Practice
QuickXsort is a highly efficient inplace sequential sorting scheme that...
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NearlyOptimal Mergesorts: Fast, Practical Sorting Methods That Optimally Adapt to Existing Runs
We present two stable mergesort variants, "peeksort" and "powersort", th...
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Most abundant isotope peaks and efficient selection on Y=X_1+X_2+... + X_m
The isotope masses and relative abundances for each element are fundamen...
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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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The SaukasSong Selection Algorithm and Coarse Grained Parallel Sorting
We analyze the running time of the SaukasSong algorithm for selection o...
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On the WorstCase Complexity of TimSort
TimSort is an intriguing sorting algorithm designed in 2002 for Python, ...
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Oblivious Median Slope Selection
We study the median slope selection problem in the oblivious RAM model. ...
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QuickMergesort: Practically Efficient ConstantFactor Optimal Sorting
We consider the fundamental problem of internally sorting a sequence of n elements. In its best theoretical setting QuickMergesort, a combination Quicksort with Mergesort with a Medianof√(n) pivot selection, requires at most n n  1.3999n + o(n) element comparisons on the average. The questions addressed in this paper is how to make this algorithm practical. As refined pivot selection usually adds much overhead, we show that the Medianof3 pivot selection of QuickMergesort leads to at most n n  0.75n + o(n) element comparisons on average, while running fast on elementary data. The experiments show that QuickMergesort outperforms stateoftheart library implementations, including C++'s Introsort and Java's DualPivot Quicksort. Further tradeoffs between a low running time and a low number of comparisons are studied. Moreover, we describe a practically efficient version with n n + O(n) comparisons in the worst case.
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