Related papers: weberknecht -- a One-Sided Crossing Minimization s…
This paper discusses a class of combinatorial optimization problems with uncertain costs in the objective function. It is assumed that a sample of the cost realizations is available, which defines an empirical probability distribution for…
We are interested in computing the treewidth $\tw(G)$ of a given graph $G$. Our approach is to design heuristic algorithms for computing a sequence of improving upper bounds and a sequence of improving lower bounds, which would hopefully…
We propose a new approximate series solution of the semiclassical Wigner equation by uniformization of WKB approximations of the Schr\"odinger eigenfunctions.
We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal…
We propose a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-length Minimization Search (VeRMinS). Basically, it constitutes of a re-casting of the…
The independent solutions of the one-dimensional Schr\"odinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the fixed point iterations is…
We present a new heuristic method for minimising crossings in a graph. The method is based upon repeatedly solving the so-called {\em star insertion problem} in the setting where the combinatorial embedding is fixed, and has several…
The Wasserstein metric is broadly used in optimal transport for comparing two probabilistic distributions, with successful applications in various fields such as machine learning, signal processing, seismic inversion, etc. Nevertheless, the…
This paper is dedicated to the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the highly oscillatory regime. We compute an approximate solution based on the well-known WKB-ansatz, which relies on…
We provide an iterative solution approach for the indefinite Helmholtz equation discretised using finite elements, based upon a Hermitian Skew-Hermitian Splitting (HSS) iteration applied to the shifted operator, and prove that the iteration…
The 2024 PACE Challenge focused on the One-Sided Crossing Minimization (OCM) problem, which aims to minimize edge crossings in a bipartite graph with a fixed order in one partition and a free order in the other. We describe our OCM solver…
A resolving set in a graph $G$ is a vertex subset $W= \{\omega^1, \dots, \omega^n\} \subseteq V(G)$ such that each $u \in V(G)$ can be uniquely identified by the vector $r(u \vert W) = (d(u,\omega^1), \dots, d(u,\omega^n))$ of metric…
The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods.…
In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial…
Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when…
The considered problem is how to optimally allocate a set of jobs to technicians of different skills such that the number of technicians of each skill does not exceed the number of persons with that skill designation. The key motivation is…