Related papers: Analysis of Pivot Sampling in Dual-Pivot Quicksort

We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…

The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of $n$ data, permuted uniformly at random, the appropriately normalized complexity $Y_n$ is…

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…

We present a stable mergesort variant, Multiway Powersort, that exploits existing runs and finds nearly-optimal merging orders for k-way merges with negligible overhead. This builds on Powersort (Munro & Wild, ESA2018), which has recently…

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…

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…

We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing…

Many statistical problems and applications require repeated computation of order statistics, such as the median, but most statistical and programming environments do not offer in their main distribution linear selection algorithms. We…

We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…

Conventional sorting algorithms make use of such data structures as array, file and list which define access methods of the items to be sorted. Such traditional methods as exchange sort, divide and conquer sort, selection sort and insertion…

I prove that the average number of comparisons for median-of-$k$ Quicksort (with fat-pivot a.k.a. three-way partitioning) is asymptotically only a constant $\alpha_k$ times worse than the lower bound for sorting random multisets with…

Database applications are increasingly bottlenecked by memory bandwidth and latency due to the memory wall and the limited scalability of DRAM. Join queries, central to analytical workloads, require intensive memory access and are…

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…

Consensus clustering (or clustering aggregation) inputs $k$ partitions of a given ground set $V$, and seeks to create a single partition that minimizes disagreement with all input partitions. State-of-the-art algorithms for consensus…

Semisort is a fundamental algorithmic primitive widely used in the design and analysis of efficient parallel algorithms. It takes input as an array of records and a function extracting a \emph{key} per record, and reorders them so that…

This work aims to improve the sample efficiency of parallel large-scale ranking and selection (R&S) problems by leveraging correlation information. We modify the commonly used "divide and conquer" framework in parallel computing by adding a…

Priority queues are data structures that maintain a dynamic collection of elements and allow inserting new elements and removing the smallest element. The most widely known and used priority queue is likely the implicit binary heap, even…

Suppose we have a memory storing $0$s and $1$s and we want to estimate the frequency of $1$s by sampling. We want to do this I/O-efficiently, exploiting that each read gives a block of $B$ bits at unit cost; not just one bit. If the input…

The attention module in vision transformers(ViTs) performs intricate spatial correlations, contributing significantly to accuracy and delay. It is thereby important to modulate the number of attentions according to the input feature…

Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…