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arXiv · 2604.21248

Optimum adaptation of a Steiner network

Manou Rosenberg·Mengbin Ye·Brian D. O. Anderson
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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.

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Manou Rosenberg, Mengbin Ye, Brian D. O. Anderson. 2026-04-23. Optimum adaptation of a Steiner network. https://arxiv.org/abs/2604.21248

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