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Intersection graphs are well-studied in the area of graph algorithms. Some intersection graph classes are known to have algorithms enumerating all unlabeled graphs by reverse search. Since these algorithms output graphs one by one and the…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
Uncertainties such as manufacturing tolerances cause performance variations in complex engineering systems, making robust design optimization (RDO) essential. However, simulation-based RDO faces high computational cost for statistical…
We study the worst-case behavior of Block Coordinate Descent (BCD) type algorithms for unconstrained minimization of coordinate-wise smooth convex functions. This behavior is indeed not completely understood, and the practical success of…
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…
In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…
In the first part of the paper we present a short review of applications of digital differential analyzers (DDA) to generation of circles showing that they can be treated as one-step numerical schemes. In the second part we present and…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Error-tolerant applications, such as multimedia processing, machine learning, signal processing, and scientific computing, can produce satisfactory outputs even when approximate computations are performed. Approximate computing (AxC) is…
Random permutation is observed to be powerful for optimization algorithms: for multi-block ADMM (alternating direction method of multipliers), while the classical cyclic version divergence, the randomly permuted version converges in…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…
The BCD (Binary Coded Decimal) being the more accurate and human-readable representation with ease of conversion, is prevailing in the computing and electronic communication.In this paper, a tree-structured parallel BCD addition algorithm…
Stochastic gradient descent-based algorithms are widely used for training deep neural networks but often suffer from slow convergence. To address the challenge, we leverage the framework of the alternating direction method of multipliers…