A Note on: `Algorithms for Connected Set Cover Problem and Fault-Tolerant Connected Set Cover Problem'

TL;DR

This paper corrects a flaw in a greedy algorithm for the minimum connected set cover problem and establishes a stronger approximation ratio, aligning results with related problems like connected dominating set.

Contribution

It fixes a flaw in Zhang et al.'s greedy algorithm and improves its approximation ratio for the connected set cover problem.

Findings

Corrected the greedy algorithm for minimum connected set cover

Established a stronger approximation ratio

Results align with connected dominating set problem

Abstract

A flaw in the greedy approximation algorithm proposed by Zhang et al. for minimum connected set cover problem is corrected, and a stronger result on the approximation ratio of the modified greedy algorithm is established. The results are now consistent with the existing results on connected dominating set problem which is a special case of the minimum connected set cover problem.