Related papers: Dual pivot Quicksort
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational…
Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Tipping points occur in many real-world systems, at which the system shifts suddenly from one state to another. The ability to predict the occurrence of tipping points from time series data remains an outstanding challenge and a major…
The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…
This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…
In the recent decade companies started collecting of large amount of data. Without a proper analyse, the data are usually useless. The field of analysing the data is called data mining. Unfortunately, the amount of data is quite large: the…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
The number of comparisons X_n used by Quicksort to sort an array of n distinct numbers has mean mu_n of order n log n and standard deviation of order n. Using different methods, Regnier and Roesler each showed that the normalized variate…
In this paper, we derive the algorithm for calculating the normal form of the double Hopf bifurcation that appears in a memory-based diffusion system via taking memory-based diffusion coefficient and the memory delay as the perturbation…
We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the…
When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…