Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi-marginal GW transport. The former can reduce the computational complexity when computing all GW distances of a large set of inputs. The latter allows for a simultaneous matching of more than two marginals, which can for example be used to compute GW barycenters. The aim of this paper is to show an approximation result which characterizes the linear version as a limit of a multi-marginal GW formulation.

翻译：最近,最佳运输理论的两个概念已成功地带到Gromov-Wasserstein (GW) 设置上, 引入了GW 距离和多边GW 传输的线性版本。 前者在计算大量输入的所有 GW 距离时可以降低计算复杂性。 后者允许同时匹配两个以上的边际, 例如可用于计算 GW 信标。 本文的目的是显示一个近似结果, 将线性版本定性为多边际 GW 配方的限度 。