QuickHeapsort, an efficient mix of classical sorting algorithms

Cantone, Domenico; Cincotti, Gianluca

doi:10.1016/s0304-3975(01)00288-2

Cited by 18 publications

(30 citation statements)

References 12 publications

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“…We also implemented QuickMergesort with median of three for pivot selection, which turns out to be practically efficient, although it needs slightly more comparisons than QuickMergesort with median of √ n. However, 1 Our experiments were run on one core of an Intel Core i7-3770 CPU (3.40GHz, 8MB Cache) with 32GB RAM; Operating system: Ubuntu Linux 64bit; Compiler: GNU's g++ (version 4.6.3) optimized with flag -O3. 2 To rely on objects being handled we avoided the flattening of the array structure by the compiler. Hence, for the running time experiments, and in each comparison taken, we left the counter increase operation intact.…”

Section: Methodsmentioning

confidence: 99%

“…Based on QuickHeapsort [2], we develop the concept of QuickXsort in this paper and apply it to Mergesort and WeakHeapsort, what yields efficient internal sorting algorithms. The idea is very simple: as in Quicksort the array is partitioned into the elements greater and less than some pivot element.…”

Section: Introductionmentioning

confidence: 99%

“…Finding the median means significant additional effort. Cantone and Cincotti [2] weakened the requirement for the pivot and designed QuickHeapsort which uses only a sample of smaller size to select the pivot for partitioning. UltimateHeapsort is inferior to QuickHeapsort in terms of average case number of comparisons, although, unlike QuickHeapsort, it allows an n log n + O(n) bound for the worst case number of comparisons.…”

Section: Introductionmentioning

confidence: 99%

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QuickXsort: Efficient Sorting with n logn − 1.399n + o(n) Comparisons on Average

Edelkamp

Weiß

2014

Computer Science - Theory and Applications

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In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions. We show that up to o(n) terms the average number of comparisons incurred by QuickXsort is equal to the average number of comparisons of X.We also describe a new variant of WeakHeapsort. With QuickWeak-Heapsort and QuickMergesort we present two examples for the QuickXsort construction. Both are efficient algorithms that perform approximately n log n − 1.26n + o(n) comparisons on average. Moreover, we show that this bound also holds for a slight modification which guarantees an n log n + O(n) bound for the worst case number of comparisons.Finally, we describe an implementation of MergeInsertion and analyze its average case behavior. Taking MergeInsertion as a base case for QuickMergesort, we establish an efficient internal sorting algorithm calling for at most n log n − 1.3999n + o(n) comparisons on average. QuickMergesort with constant size base cases shows the best performance on practical inputs and is competitive to STL-Introsort.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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QuickXsort: Efficient Sorting with n logn − 1.399n + o(n) Comparisons on Average

Edelkamp

Weiß

2014

Computer Science - Theory and Applications

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“…Recently, in [16], the idea of QuickHeapsort [2,5] was generalized to the notion of QuickXsort: Given some black-box sorting algorithm X, QuickXsort can be used to speed X up provided that X satisfies certain natural conditions. QuickWeakHeapsort and QuickMergesort were described as two examples of this construction.…”

Section: Constant-factor-optimal Sortingmentioning

confidence: 99%

Weak Heaps and Friends: Recent Developments

Edelkamp

Elmasry

Katajainen

et al. 2013

Lecture Notes in Computer Science

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In its elementary form, a priority queue is a data structure that stores a collection of elements and supports the operations construct, minimum, insert, and extract-min [4]. In applications where this set of operations is sufficient, the priority queue that the users would select is a binary heap [29] or a weak heap [7]. Both of these data structures are known to perform well, and in typical cases the difference in performance is marginal. Most library implementations are based on a binary heap. However, one reason why a user might vote for a weak heap over a binary heap is that weak heaps are known to perform less element comparisons in the worst case: Comparing binary heaps vs. weak heaps for construct we have 2n vs. n − 1 and for extract-min we have 2 lg n vs. lg n

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“…QuickHeapsort is a combination of Quicksort and Heapsort which was first described by Cantone and Cincotti [2]. It is based on Katajainen's idea for Ultimate Heapsort [12].…”

Section: Introductionmentioning

confidence: 99%

QuickHeapsort: Modifications and Improved Analysis

Diekert

Weiß

2013

Computer Science – Theory and Applications

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We present a new analysis for QuickHeapsort splitting it into the analysis of the partition-phases and the analysis of the heap-phases. This enables us to consider samples of non-constant size for the pivot selection and leads to better theoretical bounds for the algorithm.Furthermore we introduce some modifications of QuickHeapsort, both in-place and using n extra bits. We show that on every input the expected number of comparisons is n lg n − 0.03n + o(n) (in-place) respectively n lg n − 0.997n + o(n) (always lg n = lg 2 n). Both estimates improve the previously known best results. (It is conjectured [19] that the in-place algorithm Bottom-Up-Heapsort uses at most n lg n + 0.4n on average and for Weak-Heapsort which uses n extra bits the average number of comparisons is at most n lg n − 0.42n [8].) Moreover, our non-in-place variant can even compete with index based Heapsort variants (e.g. Rank-Heapsort [17]) and Relaxed-Weak-Heapsort (n lg n − 0.9n + o(n) comparisons in the worst case) for which no O(n)-bound on the number of extra bits is known.

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QuickHeapsort, an efficient mix of classical sorting algorithms

Cited by 18 publications

References 12 publications

QuickXsort: Efficient Sorting with n logn − 1.399n + o(n) Comparisons on Average

QuickXsort: Efficient Sorting with n logn − 1.399n + o(n) Comparisons on Average

Weak Heaps and Friends: Recent Developments

QuickHeapsort: Modifications and Improved Analysis

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