Related papers: How Good is Multi-Pivot Quicksort?
The two most prominent solutions for the sorting problem are Quicksort and Mergesort. While Quicksort is very fast on average, Mergesort additionally gives worst-case guarantees, but needs extra space for a linear number of elements.…
The linear pivot selection algorithm, known as median-of-medians, makes the worst case complexity of quicksort be $\mathrm{O}(n\ln n)$. Nevertheless, it has often been said that this algorithm is too expensive to use in quicksort. In this…
The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand,…
We provide a smoothed analysis of Hoare's find algorithm and we revisit the smoothed analysis of quicksort. Hoare's find algorithm - often called quickselect - is an easy-to-implement algorithm for finding the k-th smallest element of a…
Modern comparison sorts like quicksort suffer from performance inconsistencies due to suboptimal pivot selection, leading to $(O(N^2))$ worst-case complexity, while in-place merge sort variants face challenges with data movement overhead.…
We present numerical results for the probability of bad cases for Quicksort, i.e. cases of input data for which the sorting cost considerably exceeds that of the average. Dynamic programming was used to compute solutions of the recurrence…
Sorting is one of the most basic algorithms, and developing highly parallel sorting programs is becoming increasingly important in high-performance computing because the number of CPU cores per node in modern supercomputers tends to…
An industrial grade Quicksort function along with its new algorithm is presented. Compared to 4 other well known implementations of Quicksort, the new algorithm reduces both the number of comparisons and swaps in most cases while staying…
Since the work of Kaligosi and Sanders (2006), it is well-known that Quicksort -- which is commonly considered as one of the fastest in-place sorting algorithms -- suffers in an essential way from branch mispredictions. We present a novel…
Recent works showed that implementations of Quicksort using vector CPU instructions can outperform the non-vectorized algorithms in widespread use. However, these implementations are typically single-threaded, implemented for a particular…
Sorting is one of the oldest computing problems and is still very important in the age of big data. Various algorithms and implementation techniques have been proposed. In this study, we focus on comparison based, internal sorting…
Using non-linear difference equations, combined with symbolic computations, we make a detailed study of the running times of numerous variants of the celebrated Quicksort algorithms, where we consider the variants of single-pivot and…
This paper gives a straightforward self-contained proof of the formula for the variance of the number of comparisons used by the Quicksort sorting algorithm when pivots are chosen uniformly at random. The result has been known for some time…
The modern CPU's design, which is composed of hierarchical memory and SIMD/vectorization capability, governs the potential for algorithms to be transformed into efficient implementations. The release of the AVX-512 changed things radically,…
We present an average case analysis of a variant of dual-pivot quicksort. We show that the used algorithmic partitioning strategy is optimal, i.e., it minimizes the expected number of key comparisons. For the analysis, we calculate the…
This paper presents simple variants of the BlockQuicksort algorithm described by Edelkamp and Weiss (ESA 2016). The simplification is achieved by using Lomuto's partitioning scheme instead of Hoare's crossing pointer technique to partition…
Smart Sort algorithm is a "smart" fusion of heap construction procedures (of Heap sort algorithm) into the conventional "Partition" function (of Quick sort algorithm) resulting in a robust version of Quick sort algorithm. We have also…
Multisplit is a broadly useful parallel primitive that permutes its input data into contiguous buckets or bins, where the function that categorizes an element into a bucket is provided by the programmer. Due to the lack of an efficient…
We present four high performance hybrid sorting methods developed for various parallel platforms: shared memory multiprocessors, distributed multiprocessors, and clusters taking advantage of existence of both shared and distributed memory.…
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…