${\mathcal {W}}_\infty $-transport with discrete target as a combinatorial matching problem
${\mathcal {W}}_\infty $-transport with discrete target as a combinatorial matching problem
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${mathcal {W}}_infty $-离散目标传输作为组合匹配问题
DOI：
10.1007/s00013-021-01606-z
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发表时间：
2021
影响因子：
0.6
通讯作者：
Kitagawa, Jun
中科院分区：
文献类型：
--
作者：
Bansil, Mohit;Kitagawa, Jun
在这篇简短的说明中，我们表明，给定成本函数c，两个概率度量的任何耦合（其中第二个是离散度量）都可以基于无穷大运输成本的值与包含完美匹配的特定二部图相关联。耦合和二分图之间的这种对应关系是显式构建的。当目标测量是离散时，我们将此结果应用于最优运输问题，第一个是确保映射引起的最优计划存在的条件，第二个是逼近最优计划的数值方法。
In this short note, we show that given a cost functionc, any couplingof 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. This correspondence between couplings and bipartite graphs is explicitly constructed. We give two applications of this result to theoptimal 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.