近最小生成树：概率模型中的尺度指数
Near-Minimal Spanning Trees: a Scaling Exponent in Probability Models
摘要：
本文研究了在任意点上的最小生成树（MST）与最优的“近最小”树之间的关系，即在约束条件下，最优树的边的比例$δ$必须与MST的边的比例不同。启发式方法表明，不管概率模型的细节如何，长度的比例应该是$1 + Θ(δ^2)$。我们证明了随机边长的晶格模型和欧几里德模型中的缩放结果。
英文摘要：
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $δ$ of its edges must be different from those of the MST. Heuristics suggest that, regardless of details of the probability model, the ratio of lengths should scale as $1 + Θ(δ^2)$. We prove this scaling result in the model of the lattice with random edge-lengths and in the Euclidean model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
