Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree

📰 ArXiv cs.AI

Randomized HyperSteiner is a stochastic Delaunay triangulation heuristic for constructing Steiner Minimal Trees in hyperbolic space

advanced Published 31 Mar 2026

Action Steps

Construct a Delaunay triangulation of the input points in hyperbolic space
Incorporate randomness into the expansion process to avoid locally suboptimal configurations
Refine candidate trees via Riemannian optimization
Evaluate the quality of the resulting Steiner Minimal Tree using metrics such as tree length or node count

Who Needs to Know This

This research benefits machine learning engineers and researchers working on geometric deep learning and computational geometry, as it provides a new approach to solving the Steiner Minimal Tree problem in hyperbolic space

Key Insight

💡 Incorporating randomness into the expansion process can help avoid locally suboptimal configurations and improve the quality of the resulting Steiner Minimal Tree

Key Takeaways

Randomized HyperSteiner is a stochastic Delaunay triangulation heuristic for constructing Steiner Minimal Trees in hyperbolic space

Full Article

Title: Randomized HyperSteiner: A Stochastic Delaunay Triangulation Heuristic for the Hyperbolic Steiner Minimal Tree

Abstract:
arXiv:2510.09328v2 Announce Type: replace-cross Abstract: We study the problem of constructing Steiner Minimal Trees (SMTs) in hyperbolic space. Exact SMT computation is NP-hard, and existing hyperbolic heuristics such as HyperSteiner are deterministic and often get trapped in locally suboptimal configurations. We introduce Randomized HyperSteiner (RHS), a stochastic Delaunay triangulation heuristic that incorporates randomness into the expansion process and refines candidate trees via Riemannia

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