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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 theMin-Power $k$ Edge Disjoint $st$-Paths problem $F$ should contains $k$ edgedisjoint $st$-paths. The problem admits a $k$-approximation algorithm, and itwas an open question whether it admits approximation ratio sublinear in $k$even for unit costs. We give a $4\sqrt{2k}$-approximation algorithm for generalcosts.

An $O(\sqrt{k})$-approximation algorithm for minimum power $k$ edge disjoint $st$ -paths