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 form 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

如果供应图与需求边形成平面图，我们为边不相交路径问题的最大化版本设计了一个常数因子近似算法。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。