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An $2\sqrt{k}$-approximation algorithm for minimum power $k$ edge disjoint $st$ -paths (2208.09373v2)
Published 19 Aug 2022 in cs.DS
Abstract: 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.
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