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Near-Minimal Spanning Trees: a Scaling Exponent in Probability Models

David Aldous·Charles Bordenave·Marc Lelarge
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Abstract

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.

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David Aldous, Charles Bordenave, Marc Lelarge. 2007-07-23. Near-Minimal Spanning Trees: a Scaling Exponent in Probability Models. https://arxiv.org/abs/math/0609547

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