An $\tilde{O}(\log^2 n)$-approximation algorithm for $2$-edge-connected dominating set

TL;DR

This paper introduces the first non-trivial approximation algorithm for the 2-edge-connected dominating set problem, achieving an expected ratio of approximately logarithmic squared in the number of vertices.

Contribution

It presents the first known approximation algorithm for the 2-edge-connected dominating set problem with a ratio of O(log^2 n), advancing the understanding of this computational challenge.

Findings

Provides the first non-trivial approximation algorithm for the problem.

Achieves an expected approximation ratio of O(log^2 n).

Establishes a new benchmark for approximation in 2-edge-connected dominating set problems.

Abstract

In the Connected Dominating Set problem we are given a graph $G=(V,E)$ and seek a minimum size dominating set $S \subseteq V$ such that the subgraph $G[S]$ of $G$ induced by $S$ is connected. In the $2$-Edge-Connected Dominating Set problem $G[S]$ should be $2$-edge-connected. We give the first non-trivial approximation algorithm for this problem, with expected approximation ratio $\tilde{O}(\log^2n)$.