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Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…

Data Structures and Algorithms · Computer Science 2011-05-18 William F. Gilreath

Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring us. This paper provides a…

Optimization and Control · Mathematics 2017-05-23 Xiangru Lian , Huan Zhang , Cho-Jui Hsieh , Yijun Huang , Ji Liu

Sorting is a fundamental problem in computer science. In the classical setting, it is well-known that $(1\pm o(1)) n\log_2 n$ comparisons are both necessary and sufficient to sort a list of $n$ elements. In this paper, we study the Noisy…

Data Structures and Algorithms · Computer Science 2023-03-16 Yuzhou Gu , Yinzhan Xu

We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…

Data Structures and Algorithms · Computer Science 2025-04-24 Jonathan Landers

We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…

Symbolic Computation · Computer Science 2014-02-17 Jean-Guillaume Dumas , Thierry Gautier , Clément Pernet , Ziad Sultan

Today, very large amounts of data are produced and stored in all branches of society including science. Mining these data meaningfully has become a considerable challenge and is of the broadest possible interest. The size, both in numbers…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-06-11 Andreas Vitalis

A sorted set (or map) is one of the most used data types in computer science. In addition to standard set operations, like Insert, Remove, and Contains, it can provide set-set operations such as Union,Intersection, and Difference. Each of…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-06-27 Ilya Kokorin , Vitaly Aksenov , Alena Martsenyuk

We study the problem of computing a longest increasing subsequence in a sequence $S$ of $n$ distinct elements in the presence of persistent comparison errors. In this model, every comparison between two elements can return the wrong result…

Data Structures and Algorithms · Computer Science 2018-08-13 Barbara Geissmann

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

Machine Learning · Computer Science 2014-10-24 Jingbo Shang , Tianqi Chen , Hang Li , Zhengdong Lu , Yong Yu

The evolution in the design of modern parallel platforms leads to revisit the scheduling jobs on distributed heterogeneous resources. The goal of this survey is to present the main existing algorithms, to classify them based on their…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-31 Olivier Beaumont , Louis-claude Canon , Lionel Eyraud-Dubois , Giorgio Lucarelli , Loris Marchal , Clément Mommessin , Bertrand Simon , Denis Trystram

In this paper we address the problem of designing an interruptible system in a setting in which $n$ problem instances, all equally important, must be solved concurrently. The system involves scheduling executions of contract algorithms…

Data Structures and Algorithms · Computer Science 2018-10-29 Spyros Angelopoulos , Alejandro Lopez-Ortiz

Concurrency, the art of doing many things at the same time is slowly becoming a science. It is very difficult to master, yet it arises all over modern computing systems, both when the communication medium is shared memory and when it is by…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-12-17 Sergio Rajsbaum , Michel Raynal

In the area of Pattern Recognition and Matching, finding a Longest Common Subsequence plays an important role. In this paper, we have proposed one algorithm based on parallel computation. We have used OpenMP API package as middleware to…

Data Structures and Algorithms · Computer Science 2013-06-20 Tirtharaj Dash , Tanistha Nayak

Recently, the predicate detection problem was shown to be in the parallel complexity class NC. In this paper, we give the first work-optimal parallel algorithm to solve the predicate detection problem on a distributed computation with $n$…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-03 Rohan Garg

We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-11-20 Marcos Amaris , Giorgio Lucarelli , Clément Mommessin , Denis Trystram

We consider the Pm || Cmax scheduling problem where the goal is to schedule n jobs on m identical parallel machines to minimize makespan. We revisit the famous Longest Processing Time (LPT) rule proposed by Graham in 1969. LPT requires to…

Data Structures and Algorithms · Computer Science 2018-01-18 Federico Della Croce , Rosario Scatamacchia

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing…

Data Structures and Algorithms · Computer Science 2014-05-07 Abhishek Awasthi , Jörg Lässig , Oliver Kramer

High Performance Computing (HPC) aims at providing reasonably fast computing solutions to scientific and real life problems. The advent of multicore architectures is noticeable in the HPC history, because it has brought the underlying…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-07 Claude Tadonki

Cloud database systems, particularly their middleware and query execution layers, use sorting as a core operation in query processing, indexing and join execution. Distribution-dependence and limited parallelism are key issues inherent in…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-13 Michael Dang'ana

We present and analyze a parallel implementation of a parallel-in-time collocation method based on $\alpha$-circulant preconditioned Richardson iterations. While many papers explore this family of single-level, time-parallel "all-at-once"…

Numerical Analysis · Mathematics 2023-02-16 Gayatri Caklovic , Robert Speck , Martin Frank