Related papers: How Good is Multi-Pivot Quicksort?
In this paper, a sorting technique is presented that takes as input a data set whose primary key domain is known to the sorting algorithm, and works with an time efficiency of O(n+k), where k is the primary key domain. It is shown that the…
This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data…
This paper presents a practical GPU-accelerated convex hull algorithm and a novel Sorting-based Preprocessing Approach (SPA) for planar point sets. The proposed algorithm consists of two stages: (1) two rounds of preprocessing performed on…
Adaptive indexing is a concept that considers index creation in databases as a by-product of query processing; as opposed to traditional full index creation where the indexing effort is performed up front before answering any queries.…
TimSort is an intriguing sorting algorithm designed in 2002 for Python, whose worst-case complexity was announced, but not proved until our recent preprint. In fact, there are two slightly different versions of TimSort that are currently…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Karp et al. (1988) described Deferred Data Structures for Multisets as "lazy" data structures which partially sort data to support online rank and select queries, with the minimum amount of work in the worst case over instances of size $n$…
In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick Sort. In our first study in this paper, we reconfirm this through computer experiments…
Quicksort is a classical divide-and-conquer sorting algorithm. It is a comparison sort that makes an average of $2(n+1)H_n - 4n$ comparisons on an array of size $n$ ordered uniformly at random, where $H_n = \sum_{i=1}^n\frac{1}{i}$ is the…
Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…
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…
The objective behind the Twin Sort technique is to sort the list of unordered data elements efficiently and to allow efficient and simple arrangement of data elements within the data structure with optimization of comparisons and iterations…
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…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
An inherently parallel algorithm is proposed that efficiently performs selection: finding the K-th largest member of a set of N members. Selection is a common component of many more complex algorithms and therefore is a widely studied…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…
We present a comparison of different multigrid approaches for the solution of systems arising from high-order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the…
Estimating the selectivity of a query is a key step in almost any cost-based query optimizer. Most of today's databases rely on histograms or samples that are periodically refreshed by re-scanning the data as the underlying data changes.…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…