An Improved Approximation Algorithm for the Minimum $k$-Edge Connected Multi-Subgraph Problem

TL;DR

This paper presents a new randomized approximation algorithm for the minimum $k$-edge connected spanning multi-subgraph problem, achieving a performance ratio that improves as $k$ increases.

Contribution

The paper introduces a novel randomized approximation algorithm with a ratio of $1 + rac{5.06}{\sqrt{k}}$ for the $k$-ECSM problem, improving upon previous methods.

Findings

Achieves a $1 + rac{5.06}{\sqrt{k}}$ approximation ratio.

Provides theoretical analysis of the approximation guarantee.

Applicable for large values of $k$ to obtain near-optimal solutions.

Abstract

We give a randomized $1+\frac{5.06}{\sqrt{k}}$-approximation algorithm for the minimum $k$-edge connected spanning multi-subgraph problem, $k$-ECSM.