论文标题
$ \ MATHCAL {W} _ \ infty $ -transport以离散目标作为组合匹配问题
$\mathcal{W}_\infty$-transport with discrete target as a combinatorial matching problem
论文作者
论文摘要
在此简短说明中，我们表明，给定成本函数$ c $，即两种概率度量的$π$，其中第二个是一个离散度量的措施，可以与包含完美匹配的某个双方图相关联，基于Infinity Transport Cof的价值$ \ NORM \ norm {c} _ {c} _ {c} _ {l^\ iffty（π）} $。耦合和两分图之间的对应关系是明确构建的。我们将此结果的两个应用程序提供给$ \ MATHCAL {W} _ \ INSTCAL $最佳传输问题时，当目标度量离散时，第一个是确保存在由映射引起的最佳计划的条件，第二个是一种数值方法，是一种近似最佳计划的数值方法。
In this short note, we show that given a cost function $c$, any coupling $π$ of two probability measures where the second is a discrete measure can be associated to a certain bipartite graph containing a perfect matching, based on the value of the infinity transport cost $\norm{c}_{L^\infty(π)}$. This correspondence between couplings and bipartite graphs is explicitly constructed. We give two applications of this result to the $\mathcal{W}_\infty$ optimal transport problem when the target measure is discrete, the first is a condition to ensure existence of an optimal plan induced by a mapping, and the second is a numerical approach to approximating optimal plans.
