Near-Optimal Distributed Approximation of Minimum-Weight Connected Dominating Set

TL;DR

This paper introduces a near-optimal distributed algorithm for the minimum-weight connected dominating set problem, achieving an $O(rac{ ext{log} n}{ ext{approximation}})$ factor in near-optimal rounds, advancing theoretical understanding of distributed network optimization.

Contribution

It provides a distributed algorithm with near-optimal approximation ratio and round complexity for MCDS, matching known lower bounds up to logarithmic factors.

Findings

Achieves $O( ext{log} n)$ approximation for MCDS.

Runs in $ ilde{O}(D+ ext{sqrt}(n))$ rounds, near the lower bound.

Proves the optimality of the approximation and complexity bounds.

Abstract

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. MCDS is a classical NP-hard problem and the achieved approximation factor $O(\log n)$ is known to be optimal up to a constant factor, unless P=NP. Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be optimal modulo logarithmic factors (for any approximation), following [Das Sarma et al.---STOC'11].