An Evolver program for weighted Steiner trees

TL;DR

This paper introduces a compact algorithm implemented in Evolver for approximating weighted Steiner minimal trees, mimicking physical soap film experiments and comparing favorably with existing methods in certain cases.

Contribution

The paper presents a concise, energy-based algorithm in Evolver for weighted Steiner trees, integrating physical simulation and minimal code for near-optimal solutions.

Findings

Reproduces soap film detachment behavior

Achieves near-optimal solutions with 183 lines of code

Compares favorably with GeoSteiner in specific patterns

Abstract

We present an algorithm to find near-optimal weighted Steiner minimal trees in the plane. The algorithm is implemented in Evolver programming language, which already contains many built-in energy minimisation routines. Some are invoked in the program, which enable it to consist of only 183 lines of source code. Our algorithm reproduces the physical experiment of a soap film detaching from connected pins towards a stable configuration. In the non-weighted case comparisons with GeoSteiner are drawn for terminals that form a pattern.