Combinatorial optimization over two random point sets

TL;DR

This paper studies the asymptotic behavior of combinatorial optimization problems involving two large random point sets, focusing on the convergence of minimal solutions like matchings and tours as the set size grows.

Contribution

It provides a theoretical analysis of the convergence properties of bipartite combinatorial optimization functionals over large random point sets.

Findings

Convergence of minimal bipartite matchings as set size increases

Asymptotic behavior of bipartite TSP tours

Analysis of minimal length bipartite r-regular graphs

Abstract

We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set, or the connected bipartite r-regular graph of minimal length. As the cardinal of the sets goes to infinity, we investigate the convergence of such bipartite functionals.