On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Line

Robert Beinert, Cosmas Heiss, Gabriele Steidl

Let $x_1<\cdots <x_n$ and $y_1<\cdots <y_n$, $n\in \mathbb{N}$, be real numbers. We show by an example that the assignment problem $$ \max_{σ\in S_n} F_σ(x,y) := \frac12 \sum_{…