相关论文: Galloping in fast-growth natural merge sorts

We provide full certifications of two versions of merge sort of arrays in the verification-aware programming language Dafny. We start by considering schemas for applying the divide-and-conquer or partition method of solution to…

A low storage algorithm for constructing isogenies between ordinary elliptic curves was proposed by Galbraith, Hess and Smart (GHS). We give an improvement of this algorithm by modifying the pseudorandom walk so that lower-degree isogenies…

In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…

Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…

Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…

A simple and fast analysis method to sort large data sets into groups with shared distinguishing characteristics is described, and applied to single molecular break junction conductance versus electrode displacement data. The method, based…

State-of-the-art parallel sorting algorithms for distributed-memory architectures are based on computing a balanced partitioning via sampling and histogramming. By finding samples that partition the sorted keys into evenly-sized chunks,…

Groote and Wijs recently described an algorithm for deciding stuttering equivalence and branching bisimulation equivalence, acclaimed to run in $\mathcal{O}(m \log n)$ time. Unfortunately, the algorithm does not always meet the acclaimed…

Given a sequence of $n$ numbers and $k$ parallel First-in-First-Out (FIFO) queues, how close can one bring the sequence to sorted order? It is known that $k$ queues suffice to sort the sequence if the Longest Decreasing Subsequence (LDS) of…

In scientific computing, it is common that a mathematical expression can be computed by many different algorithms (sometimes over hundreds), each identifying a specific sequence of library calls. Although mathematically equivalent, those…

Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based…

We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…

The Bulk-Synchronous Parallel model of computation has been used for the architecture independent design and analysis of parallel algorithms whose performance is expressed not only in terms of problem size n but also in terms of parallel…

Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…

A new Combined Sieve algorithm is presented with cost proportional to the number of enumerated factors over a series of intervals. This algorithm achieves a significant speedup, over a traditional sieve, when handling many ([10^4, 10^7])…

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.…

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

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…

We introduce an algorithm for the uniform generation of infinite runs in concurrent systems under a partial order probabilistic semantics. We work with trace monoids as concurrency models. The algorithm outputs on-the-fly approximations of…

With the explosion of the size of digital dataset, the limiting factor for decomposition algorithms is the \emph{number of passes} over the input, as the input is often stored out-of-core or even off-site. Moreover, we're only interested in…