Optimal Transportation and Applications

Optimal transport methods for combinatorial optimization over two random point sets

speaker: Dario Trevisan (Università di Pisa)

abstract: We describe some recent results (jointly obtained with M. Goldman, arXiv:2209.14615) on the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in d-dimensional spaces, where the edge cost between two points is given by a p-th power of their Euclidean distance. These include 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≤p2. 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.

timetable:
Thu 27 Oct, 14:30 - 15:15, Aula Magna Bruno Pontecorvo
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