In minimum power network design problems we are given an undirected graph $G=(V,E)$ with edge costs $\{c_e:e \in E\}$. The goal is to find an edge set $F\subseteq E$ that satisfies a prescribed property of minimum power $p_c(F)=\sum_{v \in V} \max \{c_e: e \in F \mbox{ is incident to } v\}$. In the Min-Power $k$ Edge Disjoint $st$-Paths problem $F$ should contains $k$ edge disjoint $st$-paths. The problem admits a $k$-approximation algorithm, and it was an open question whether it admits approximation ratio sublinear in $k$ even for unit costs. We give a $2\sqrt{2k}$-approximation algorithm for general costs.

翻译：在最小功率网络设计问题中，给定一个无向图$G=(V,E)$，其边具有成本$\{c_e:e \in E\}$。目标是找到一个边集$F\subseteq E$，满足规定性质，并最小化功率$p_c(F)=\sum_{v \in V} \max \{c_e: e \in F \mbox{ 与 } v \mbox{ 关联}\}$。在最小功率$k$边不交$st$路径问题中，$F$应包含$k$条边不交的$st$路径。该问题存在一个$k$近似算法，而即使是单位成本情况下，是否存在亚线性于$k$的近似比一直是一个开放问题。我们针对一般成本给出了一个$2\sqrt{2k}$近似算法。