Near-minimal spanning trees: A scaling exponent in probability models

• Published in: Annales de l'I.H.P. Probabilités et statistiques Vol. 44; no. 5; pp. 962 - 976
• Main Authors: Aldous, David J., Bordenave, Charles, Lelarge, Marc
• Format: Journal Article
• Language: English
• Published: Institut Henri Poincaré 01.10.2008
• Subjects: 05C80; 60K35; 68W40; Combinatorial optimization; Continuum percolation; Disordered lattice; Local weak convergence; Minimal spanning tree; Poisson point process; Probabilistic analysis of algorithms; Random geometric graph

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...