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 Riemannian gradient descent optimization. Experiments on synthetic data sets and a real-world single-cell transcriptomic data show that RHS outperforms Minimum Spanning Tree (MST), Neighbour Joining, and vanilla HyperSteiner (HS). In near-boundary configurations, RHS can achieve a 32% reduction in total length over HS, demonstrating its effectiveness and robustness in diverse data regimes.

翻译：我们研究了在双曲空间中构建斯坦纳最小树的问题。精确的斯坦纳最小树计算是NP难的，现有的双曲启发式算法如HyperSteiner具有确定性，且常陷入局部次优构型。我们提出了随机化HyperSteiner，一种随机德劳内三角剖分启发式算法，它将随机性引入扩展过程，并通过黎曼梯度下降优化对候选树进行精化。在合成数据集和真实单细胞转录组数据上的实验表明，随机化HyperSteiner优于最小生成树、邻接连接法和原始HyperSteiner。在近边界构型中，随机化HyperSteiner相较于HyperSteiner可实现总长度减少32%，展示了其在多种数据场景中的有效性和鲁棒性。