By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of this algorithm is the repeated evaluation of marginals. In [Haasler et al., IEEE Trans. Inf. Theory, 67 (2021)], it has been suggested that this evaluation can be accelerated when the application features an underlying graphical model. In this work, we accelerate the computation further by combining the tensor network dual of the graphical model with additional low-rank approximations. For the color transfer of images, these added low rank approximations save more than 96% of the computation time.

翻译：通过添加成份正规化,多边最佳运输问题可以转化为成倍缩放问题,这可以通过多边Sinkhorn算法从数字上加以解决。这一算法的主要计算瓶颈是对边缘的反复评估。在[Haasler 等人, IEEE Trans. Inf. Theory, 67 (2021)]中,建议当应用程序含有一个基本图形模型时,可以加速这项评估。在这项工作中,我们进一步加快计算,将图形模型的成份网与额外的低级近似值相结合。对于图像的颜色转换,这些低级近似值增加了96%的计算时间。