Optimum adaptation of a Steiner network
Abstract
The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point or a terminal node, and with the placements minimising the sum of all the edge lengths of the associated tree. We consider a problem in which we start with a known solution to a Steiner tree problem, and the terminal positions are then perturbed. A first-order approximation theorem is established for efficiently updating the Steiner point positions to recover a Steiner tree solution after the perturbations to terminal nodes. Numerical examples illustrate the effectiveness of our approach (including a stepwise application for large perturbations) as well as its limitations.
Keywords
Cite
@article{arxiv.2604.21248,
title = {Optimum adaptation of a Steiner network},
author = {Manou Rosenberg and Mengbin Ye and Brian D. O. Anderson},
journal= {arXiv preprint arXiv:2604.21248},
year = {2026}
}
Comments
8 pages, 2 double-figures, IFAC World Congress