SIAM Journal on Discrete Mathematics, Volume 35, Issue 2, Page 752-769, January 2021.
We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges forms a planar graph. By planar duality, this is equivalent to packing cuts in a planar graph such that each cut contains exactly one demand edge. We also show that the natural linear programming relaxations have constant integrality gap, yielding an approximate max-multiflow min-multicut theorem.

中文翻译：

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完全平面边缘不相交路径的近似算法

SIAM杂志上离散数学，35卷，第2期，页752-769，2021年一月
，我们制定了边缘分离路径问题的最大化版本的恒定因素近似算法，如果用需求供给曲线一起边缘上形成了平面图。根据平面对偶性，这相当于在平面图中打包切割，使得每个切割都包含一个需求边。我们还表明自然线性规划松弛具有恒定的完整性间隙，从而产生近似的最大多流最小多割定理。