Optimal transport methods for combinatorial optimization over two random point sets - Archive ouverte HAL
Article Dans Une Revue Probability Theory and Related Fields Année : 2023

Optimal transport methods for combinatorial optimization over two random point sets

Résumé

We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in R d where the edge cost between two points is given by a p-th power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and d ≥ 3, 1 ≤ p < d. Previous results were limited to the range p < d/2. Our proofs are based on subadditivity methods and build upon new bounds for random instances of the Euclidean bipartite matching problem, obtained through its optimal transport relaxation and functional analytic techniques.
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Dates et versions

hal-03792981 , version 1 (30-09-2022)
hal-03792981 , version 2 (28-11-2023)

Identifiants

Citer

Michael Goldman, Dario Trevisan. Optimal transport methods for combinatorial optimization over two random point sets. Probability Theory and Related Fields, In press, ⟨10.1007/s00440-023-01245-1⟩. ⟨hal-03792981v2⟩
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