An $2\sqrt{k}$-approximation algorithm for minimum power $k$ edge disjoint $st$ -paths

TL;DR

This paper presents a new approximation algorithm with ratio $2\sqrt{k}$ for the minimum power $k$ edge disjoint $st$-paths problem, improving upon the known linear ratio and addressing an open question.

Contribution

The authors develop a $2\sqrt{2k}$-approximation algorithm for the problem with general costs, achieving sublinear approximation ratio in $k$.

Findings

Achieved a $2\sqrt{2k}$-approximation ratio for the problem.

Improved the approximation ratio from linear to sublinear in $k$.

Addressed an open question in the field.

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.