A 1.5-pproximation algorithms for activating 2 disjoint $st$-paths

In the $Activation$ $k$ $Disjoint$ $st$-$Paths$ ($Activation$ $k$-$DP$) problem we are given a graph $G=(V,E)$ with activation costs $\{c_{uv}^u,c_{uv}^v\}$ for every edge $uv\in E$, a source-sink pair $s,t\in V$, and an integer $k$. The goal is to compute an edge set $F\subseteq E$ of $k$ internally node disjoint $st$-paths of minimum activation cost ${\displaystyle \sum _{v\in V}\underset{uv\in E}{\max }{c}_{uv}^v}$. The problem admits an easy $2$-approximation algorithm. Alqahtani and Erlebach [CIAC, pages 1-12, 2013] claimed that Activation 2-DP admits a $1.5$-approximation algorithm. Their proof has an error, and we will show that the approximation ratio of their algorithm is at least $2$. We will then give a different algorithm with approximation ratio $1.5$.