A Sparse Multi-Scale Algorithm for Dense Optimal Transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of an algorithm to solve large dense problems by considering a sequence of sparse problems instead. The algorithm lends itself to being combined with a hierarchical multi-scale scheme. Any existing discrete solver can be used as internal black-box.Several cost functions, including the noisy squared Euclidean distance, are explicitly detailed. We observe a significant reduction of run-time and memory requirements.Comment: Published "online first" in Journal of Mathematical Imaging and Vision, see DO

An Iterative Cyclic Algorithm for Designing Vaccine Distribution Networks in Low and Middle-Income Countries

The World Health Organization's Expanded Programme on Immunization (WHO-EPI) was developed to ensure that all children have access to common childhood vaccinations. Unfortunately, because of inefficient distribution networks and cost constraints, millions of children in many low and middle-income countries still go without being vaccinated. In this paper, we formulate a mathematical programming model for the design of a typical WHO-EPI network with the goal of minimizing costs while providing the opportunity for universal coverage. Since it is only possible to solve small versions of the model optimally, we describe an iterative heuristic that cycles between solving restrictions of the original problem and show that it can find very good solutions in reasonable time for larger problems that are not directly solvable.Comment: International Joint Conference on Industrial Engineering and Operations Management- ABEPRO-ADINGOR-IISE-AIM-ASEM (IJCIEOM 2019). Novi Sad, Serbia, July 15-17t

Improved recursive Green's function formalism for quasi one-dimensional systems with realistic defects

We derive an improved version of the recursive Green's function formalism (RGF), which is a standard tool in the quantum transport theory. We consider the case of disordered quasi one-dimensional materials where the disorder is applied in form of randomly distributed realistic defects, leading to partly periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the recursive decimation scheme, using the iteration steps of the renormalization decimation algorithm. This leads to a smaller effective system, which is treated using the common forward iteration scheme. The computational complexity scales linearly with the number of defects, instead of linearly with the total system length for the conventional approach. We show that the scaling of the calculation time of the Green's function depends on the defect density of a random test system. Furthermore, we discuss the calculation time and the memory requirement of the whole transport formalism applied to defective carbon nanotubes