Approximating Minimum-Cost k-Node Connected Subgraphs via Independence-Free Graphs

TL;DR

This paper introduces a 6-approximation algorithm for the minimum-cost k-node connected subgraph problem, achieving the first constant-factor approximation for instances with sufficiently many nodes, using combinatorial preprocessing and iterative rounding.

Contribution

It presents the first constant-factor approximation algorithm for the problem in the asymptotic setting, leveraging a novel preprocessing step based on Frank-Tardos algorithm.

Findings

Achieves a 6-approximation ratio for the problem.

First constant-factor approximation in the asymptotic setting.

Uses combinatorial preprocessing to enable iterative rounding.

Abstract

We present a 6-approximation algorithm for the minimum-cost $k$-node connected spanning subgraph problem, assuming that the number of nodes is at least $k^3(k-1)+k$. We apply a combinatorial preprocessing, based on the Frank-Tardos algorithm for $k$-outconnectivity, to transform any input into an instance such that the iterative rounding method gives a 2-approximation guarantee. This is the first constant-factor approximation algorithm even in the asymptotic setting of the problem, that is, the restriction to instances where the number of nodes is lower bounded by a function of $k$.